#' -----------------------------------------------------------------------------
#' Install the new version of the package
#' -----------------------------------------------------------------------------

#library(devtools)
#install_github("lvhoskovec/mmpack", build_vignettes = TRUE, force = TRUE)

library(tidyverse)
## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──
## ✓ ggplot2 3.3.3     ✓ purrr   0.3.4
## ✓ tibble  3.0.6     ✓ dplyr   1.0.4
## ✓ tidyr   1.1.2     ✓ stringr 1.4.0
## ✓ readr   1.3.1     ✓ forcats 0.5.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()
library(lubridate)
## 
## Attaching package: 'lubridate'
## The following objects are masked from 'package:base':
## 
##     date, intersect, setdiff, union
library(haven)
library(readxl)
library(mmpack)

#' For ggplots
simple_theme <- theme(
  #aspect.ratio = 1,
  text  = element_text(family="Calibri",size = 12, color = 'black'),
  panel.spacing.y = unit(0,"cm"),
  panel.spacing.x = unit(0.25, "lines"),
  panel.grid.minor = element_line(color = "transparent"),
  panel.grid.major = element_line(color = "transparent"),
  panel.border=element_rect(fill = NA),
  panel.background=element_blank(),
  axis.ticks = element_line(colour = "black"),
  axis.text = element_text(color = "black", size=10),
  # legend.position = c(0.1,0.1),
  plot.margin=grid::unit(c(0,0,0,0), "mm"),
  legend.key = element_blank()
)
# windowsFonts(Calibri=windowsFont("TT Calibri"))
options(scipen = 9999) #avoid scientific notation

set.seed(123)

1 Sensitivty Analysis

In this version of the analysis, we are excluding race/ethnicity because the DAG may indicate the race/ethnicty are on the causal path (modifers, not confounders)

1.1 Exposure data

#' Exposure data
X <- select(hs_data2, mean_pm, mean_o3, mean_temp, pct_tree_cover, pct_impervious,
            mean_aadt_intensity, dist_m_tri:dist_m_mine_well,
            cvd_rate_adj, res_rate_adj, violent_crime_rate, property_crime_rate,
            pct_less_hs, pct_unemp, pct_limited_eng, pct_hh_pov, pct_poc) %>%
  as.matrix()
head(X)
##       mean_pm  mean_o3 mean_temp pct_tree_cover pct_impervious
## [1,] 8.483046 47.19072  51.81487       6.006276       43.30893
## [2,] 6.598608 50.05090  58.32885       7.281109       48.36432
## [3,] 7.454146 48.57052  58.01924      17.205991       31.67281
## [4,] 6.671239 50.06429  61.35590       6.842898       45.00359
## [5,] 7.122537 50.14275  59.28421       3.357792       28.16745
## [6,] 7.637453 47.03125  55.32825      10.743612       45.87564
##      mean_aadt_intensity dist_m_tri dist_m_npl dist_m_waste_site
## [1,]          10128.4962   2827.538   729.2371          4829.780
## [2,]          10749.0359   1576.420  5239.2211          4417.792
## [3,]           9048.6468   3350.303  2992.2968          5211.871
## [4,]           4223.3434   3364.954  6998.1286          8921.318
## [5,]            858.7283   2923.811  3427.2247          7006.042
## [6,]          15603.9800   3364.200  3166.5395          4484.960
##      dist_m_major_emit dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## [1,]          7968.654    29116.58        1749.1256     275.2480     155.7767
## [2,]          3780.951    51044.30        7354.5310     279.6435     226.8038
## [3,]          7423.232    36079.21        4887.2996     221.0414     157.6974
## [4,]          9636.816    42235.78        3752.6399     203.8812     142.5368
## [5,]          6806.912    29145.98         729.7784     194.1983     101.0046
## [6,]          5265.285    43921.85        5870.6867     174.3361     120.3281
##      violent_crime_rate property_crime_rate pct_less_hs pct_unemp
## [1,]          14.377133            37.32935   31.784946 11.529628
## [2,]           8.905404            67.03932   15.290231  4.908306
## [3,]           7.636888            46.78194    6.891702  4.564963
## [4,]           2.850212            21.95270    2.725915  5.623583
## [5,]           5.435988            22.49834   12.919186  5.234103
## [6,]           5.035971            47.15500    3.842365 10.000000
##      pct_limited_eng pct_hh_pov  pct_poc
## [1,]       26.114650  12.010919 90.33703
## [2,]        8.500401  18.123496 30.44025
## [3,]        0.000000   6.307978 26.63305
## [4,]        1.350621   9.292274 32.68648
## [5,]        6.307385   2.115768 73.60772
## [6,]        5.121799  25.171768 23.08698

Variance and histograms of the exposure variables (in their original units):

var(X)
##                             mean_pm        mean_o3     mean_temp pct_tree_cover
## mean_pm                 0.391784015    0.006083605    0.09741867     -0.2054297
## mean_o3                 0.006083605    9.383489039   11.72688428     -0.4158151
## mean_temp               0.097418667   11.726884276   20.59970005      0.4425544
## pct_tree_cover         -0.205429726   -0.415815089    0.44255440      9.7193077
## pct_impervious          0.508898445   -1.674151031    3.35723856      5.8719893
## mean_aadt_intensity  -182.234953786  474.627052967 2674.12174077   8431.6446632
## dist_m_tri           -255.176839682  444.286548683 -627.63132786    -73.1423054
## dist_m_npl           -289.002141382  539.849185829 -165.00509261    434.4654007
## dist_m_waste_site    -275.262105884  261.902915064   58.19389166   1933.8647304
## dist_m_major_emit      71.096593638  577.257325397  138.98687089    265.4284518
## dist_m_cafo         -1291.237441927  -35.275020052  237.89751842  10170.6234275
## dist_m_mine_well     -339.250592215 -375.434990683 -202.34883778   3136.3680766
## cvd_rate_adj            3.871688575    0.939328342    7.31791796    -24.8232924
## res_rate_adj            2.356328835   -0.181515705    7.98167422     -3.5331376
## violent_crime_rate      0.232839920    0.577648302    1.07794996     -4.0583754
## property_crime_rate     2.001989749   -2.773092354    6.06649992    -22.6429724
## pct_less_hs             1.132232861    0.637361326    0.69410116     -7.5753471
## pct_unemp               0.100439902    0.288530482    0.25729682     -0.3330523
## pct_limited_eng         0.432516169    0.295617023    0.05811301     -2.8349116
## pct_hh_pov              0.731824476   -0.606648513    0.73475917      0.3805472
## pct_poc                 1.632059580    1.202932299   -0.90133106    -19.4091792
##                     pct_impervious mean_aadt_intensity     dist_m_tri
## mean_pm                  0.5088984           -182.2350     -255.17684
## mean_o3                 -1.6741510            474.6271      444.28655
## mean_temp                3.3572386           2674.1217     -627.63133
## pct_tree_cover           5.8719893           8431.6447      -73.14231
## pct_impervious         176.8316214          55459.6063   -15279.44024
## mean_aadt_intensity  55459.6063235       67283287.0201 -1315386.69307
## dist_m_tri          -15279.4402428       -1315386.6931  6558190.20296
## dist_m_npl           -7729.3843793        1683196.0799  4282727.94125
## dist_m_waste_site    -4662.9983638        2039577.9230  2441267.84540
## dist_m_major_emit     2627.0270993        2477155.3406  1433153.16531
## dist_m_cafo          16586.9964129       15462371.9832  3431065.70215
## dist_m_mine_well       706.6674650        2073244.5987   995872.11873
## cvd_rate_adj           230.4542985          20477.4374   -49347.60273
## res_rate_adj           176.8108084          33055.3733   -31870.98664
## violent_crime_rate      26.6945028           5736.5627    -1014.08753
## property_crime_rate    118.0737725          22077.3894    -5365.69285
## pct_less_hs             56.8383947          -4056.6889   -12372.14262
## pct_unemp               25.9434246           6003.3343    -2527.22451
## pct_limited_eng         41.9919053           2620.6198    -5408.86434
## pct_hh_pov              82.2198624          17850.1649    -8842.76408
## pct_poc                 88.3560154           4526.2710   -18049.42332
##                        dist_m_npl dist_m_waste_site dist_m_major_emit
## mean_pm                 -289.0021        -275.26211          71.09659
## mean_o3                  539.8492         261.90292         577.25733
## mean_temp               -165.0051          58.19389         138.98687
## pct_tree_cover           434.4654        1933.86473         265.42845
## pct_impervious         -7729.3844       -4662.99836        2627.02710
## mean_aadt_intensity  1683196.0799     2039577.92299     2477155.34057
## dist_m_tri           4282727.9413     2441267.84540     1433153.16531
## dist_m_npl          11125411.7474     4193498.05859     6948817.25739
## dist_m_waste_site    4193498.0586     5344101.75397     1395277.06805
## dist_m_major_emit    6948817.2574     1395277.06805    10114549.72263
## dist_m_cafo          5416531.1320     5586018.82514    -2993791.05377
## dist_m_mine_well      256924.3029     1375784.78556    -1810174.74785
## cvd_rate_adj          -30921.0390      -43119.57852       16272.40152
## res_rate_adj          -19393.1304      -32402.84395       -1320.21297
## violent_crime_rate      -672.9264       -3702.61118        -360.49700
## property_crime_rate   -18283.4264      -22350.30055      -24007.42305
## pct_less_hs            -6760.5337      -11422.49855        8866.74917
## pct_unemp               2195.0515       -1476.40942        5212.74830
## pct_limited_eng          498.0033       -4277.81339        9367.28435
## pct_hh_pov             -1135.3843       -7599.74324        8682.26135
## pct_poc                -1456.8941       -8602.85207       22698.24353
##                        dist_m_cafo dist_m_mine_well   cvd_rate_adj
## mean_pm                -1291.23744        -339.2506      3.8716886
## mean_o3                  -35.27502        -375.4350      0.9393283
## mean_temp                237.89752        -202.3488      7.3179180
## pct_tree_cover         10170.62343        3136.3681    -24.8232924
## pct_impervious         16586.99641         706.6675    230.4542985
## mean_aadt_intensity 15462371.98316     2073244.5987  20477.4373759
## dist_m_tri           3431065.70215      995872.1187 -49347.6027339
## dist_m_npl           5416531.13199      256924.3029 -30921.0389720
## dist_m_waste_site    5586018.82514     1375784.7856 -43119.5785165
## dist_m_major_emit   -2993791.05377    -1810174.7478  16272.4015197
## dist_m_cafo         46324000.89481     9345575.3772 -46645.9665229
## dist_m_mine_well     9345575.37722     4430024.9964 -39046.5984701
## cvd_rate_adj          -46645.96652      -39046.5985   2039.8569530
## res_rate_adj          -13772.40263      -16322.5110   1289.5661935
## violent_crime_rate       722.31907       -2032.3464    135.9487143
## property_crime_rate   -15833.92381       -4272.3829    343.9364726
## pct_less_hs           -26060.83378      -10037.6577    328.3044447
## pct_unemp              -1030.96916       -2827.2369    105.0153846
## pct_limited_eng        -7089.15821       -4814.6687    183.5853966
## pct_hh_pov              -855.38016       -5030.4055    266.1004715
## pct_poc               -44526.37107      -24974.3303    618.2817294
##                       res_rate_adj violent_crime_rate property_crime_rate
## mean_pm                  2.3563288          0.2328399            2.001990
## mean_o3                 -0.1815157          0.5776483           -2.773092
## mean_temp                7.9816742          1.0779500            6.066500
## pct_tree_cover          -3.5331376         -4.0583754          -22.642972
## pct_impervious         176.8108084         26.6945028          118.073773
## mean_aadt_intensity  33055.3733277       5736.5627383        22077.389365
## dist_m_tri          -31870.9866403      -1014.0875345        -5365.692846
## dist_m_npl          -19393.1304345       -672.9263612       -18283.426420
## dist_m_waste_site   -32402.8439544      -3702.6111771       -22350.300554
## dist_m_major_emit    -1320.2129699       -360.4970006       -24007.423046
## dist_m_cafo         -13772.4026269        722.3190727       -15833.923813
## dist_m_mine_well    -16322.5110008      -2032.3464340        -4272.382880
## cvd_rate_adj          1289.5661935        135.9487143          343.936473
## res_rate_adj          1091.1856742        104.4979610          333.780710
## violent_crime_rate     104.4979610         40.1175363          160.725724
## property_crime_rate    333.7807097        160.7257236         1295.004010
## pct_less_hs            197.8827546         22.5579950           -3.138375
## pct_unemp               72.3576933         11.3130282            1.362247
## pct_limited_eng        104.0524036         12.7978322          -14.963510
## pct_hh_pov             201.6582659         29.1947400           64.236239
## pct_poc                297.8399442         46.4013012          -44.321973
##                        pct_less_hs     pct_unemp pct_limited_eng    pct_hh_pov
## mean_pm                  1.1322329     0.1004399      0.43251617     0.7318245
## mean_o3                  0.6373613     0.2885305      0.29561702    -0.6066485
## mean_temp                0.6941012     0.2572968      0.05811301     0.7347592
## pct_tree_cover          -7.5753471    -0.3330523     -2.83491161     0.3805472
## pct_impervious          56.8383947    25.9434246     41.99190527    82.2198624
## mean_aadt_intensity  -4056.6889048  6003.3343312   2620.61975287 17850.1649192
## dist_m_tri          -12372.1426191 -2527.2245090  -5408.86433682 -8842.7640785
## dist_m_npl           -6760.5337115  2195.0514738    498.00334199 -1135.3843390
## dist_m_waste_site   -11422.4985495 -1476.4094188  -4277.81339346 -7599.7432386
## dist_m_major_emit     8866.7491706  5212.7483023   9367.28434718  8682.2613524
## dist_m_cafo         -26060.8337755 -1030.9691591  -7089.15821141  -855.3801591
## dist_m_mine_well    -10037.6576614 -2827.2368665  -4814.66874000 -5030.4055237
## cvd_rate_adj           328.3044447   105.0153846    183.58539661   266.1004715
## res_rate_adj           197.8827546    72.3576933    104.05240356   201.6582659
## violent_crime_rate      22.5579950    11.3130282     12.79783224    29.1947400
## property_crime_rate     -3.1383751     1.3622468    -14.96351049    64.2362387
## pct_less_hs            162.1681017    39.4206217     85.19100137   100.9072175
## pct_unemp               39.4206217    24.6546969     25.21727694    36.9693212
## pct_limited_eng         85.1910014    25.2172769     68.65329426    67.2758215
## pct_hh_pov             100.9072175    36.9693212     67.27582153   119.7157808
## pct_poc                238.8801445    72.7999599    142.19618383   155.4992975
##                            pct_poc
## mean_pm                  1.6320596
## mean_o3                  1.2029323
## mean_temp               -0.9013311
## pct_tree_cover         -19.4091792
## pct_impervious          88.3560154
## mean_aadt_intensity   4526.2710457
## dist_m_tri          -18049.4233248
## dist_m_npl           -1456.8941447
## dist_m_waste_site    -8602.8520680
## dist_m_major_emit    22698.2435288
## dist_m_cafo         -44526.3710716
## dist_m_mine_well    -24974.3303024
## cvd_rate_adj           618.2817294
## res_rate_adj           297.8399442
## violent_crime_rate      46.4013012
## property_crime_rate    -44.3219731
## pct_less_hs            238.8801445
## pct_unemp               72.7999599
## pct_limited_eng        142.1961838
## pct_hh_pov             155.4992975
## pct_poc                524.7591044
ggplot(pivot_longer(as.data.frame(X), mean_pm:pct_poc, names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Scaling the exposure variables

X.scaled <- apply(X, 2, scale)
head(X.scaled)
##          mean_pm    mean_o3  mean_temp pct_tree_cover pct_impervious
## [1,]  1.60876944 -0.2502907 -0.1690421    -0.08261827      0.2084897
## [2,] -1.40186806  0.6834152  1.2661699     0.32629926      0.5886571
## [3,] -0.03503482  0.2001460  1.1979551     3.50981981     -0.6665506
## [4,] -1.28583023  0.6877893  1.9331141     0.18573791      0.3359288
## [5,] -0.56482237  0.7133998  1.4766616    -0.93215008     -0.9301550
## [6,]  0.25782234 -0.3023500  0.6050531     1.43693690      0.4015075
##      mean_aadt_intensity dist_m_tri  dist_m_npl dist_m_waste_site
## [1,]         -0.02626143 -0.4008664 -1.44212141      -0.172775897
## [2,]          0.04938980 -0.8894134 -0.08999604      -0.350992130
## [3,]         -0.15790801 -0.1967327 -0.76363997      -0.007492447
## [4,]         -0.74617032 -0.1910117  0.43733697       1.597126043
## [5,]         -1.15635722 -0.3632728 -0.63324550       0.768623456
## [6,]          0.64126566 -0.1913062 -0.71140077      -0.321936759
##      dist_m_major_emit dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## [1,]        -0.1090638  -1.1354079       -0.7748959    0.6917151   -0.2847192
## [2,]        -1.4258114   2.0863310        1.8883051    0.7890362    1.8654606
## [3,]        -0.2805619  -0.1124210        0.7160914   -0.5084805   -0.2265752
## [4,]         0.4154599   0.7921355        0.1769998   -0.8884275   -0.6855261
## [5,]        -0.4743524  -1.1310891       -1.2592010   -1.1028189   -1.9428184
## [6,]        -0.9590895   1.0398621        1.1833114   -1.5425892   -1.3578439
##      violent_crime_rate property_crime_rate pct_less_hs   pct_unemp
## [1,]          0.2444833          -0.5008789  1.20091488  0.36793456
## [2,]         -0.6194047           0.3247153 -0.09436047 -0.96557105
## [3,]         -0.8196807          -0.2382061 -0.75386917 -1.03471894
## [4,]         -1.5754111          -0.9281724 -1.08099463 -0.82151747
## [5,]         -1.1671633          -0.9130100 -0.28055077 -0.89995692
## [6,]         -1.2303189          -0.2278392 -0.99332353  0.05987409
##      pct_limited_eng pct_hh_pov    pct_poc
## [1,]      2.15383825 -0.3020187  1.5727240
## [2,]      0.02798425  0.2566428 -1.0419857
## [3,]     -0.99792447 -0.8232412 -1.2081839
## [4,]     -0.83491873 -0.5504902 -0.9439299
## [5,]     -0.23668961 -1.2063898  0.8424295
## [6,]     -0.37977738  0.9008223 -1.3629822

Variance and histograms of the exposure variables (scaled):

var(X.scaled)
##                          mean_pm      mean_o3    mean_temp pct_tree_cover
## mean_pm              1.000000000  0.003172893  0.034291650   -0.105274276
## mean_o3              0.003172893  1.000000000  0.843470729   -0.043541201
## mean_temp            0.034291650  0.843470729  1.000000000    0.031276529
## pct_tree_cover      -0.105274276 -0.043541201  0.031276529    1.000000000
## pct_impervious       0.061140333 -0.041099117  0.055625226    0.141640558
## mean_aadt_intensity -0.035493982  0.018889337  0.071828554    0.329716765
## dist_m_tri          -0.159193706  0.056635532 -0.053998558   -0.009161339
## dist_m_npl          -0.138426634  0.052836279 -0.010899557    0.041781063
## dist_m_waste_site   -0.190232937  0.036984589  0.005546380    0.268331135
## dist_m_major_emit    0.035715124  0.059253499  0.009628753    0.026770503
## dist_m_cafo         -0.303095664 -0.001691929  0.007701165    0.479321466
## dist_m_mine_well    -0.257510042 -0.058230361 -0.021182010    0.477976199
## cvd_rate_adj         0.136954783  0.006789463  0.035699097   -0.176295758
## res_rate_adj         0.113962827 -0.001793836  0.053237079   -0.034307854
## violent_crime_rate   0.058730941  0.029772424  0.037497389   -0.205526308
## property_crime_rate  0.088879773 -0.025156291  0.037142591   -0.201827442
## pct_less_hs          0.142046220  0.016338825  0.012009076   -0.190810449
## pct_unemp            0.032317153  0.018969666  0.011417056   -0.021515177
## pct_limited_eng      0.083396591  0.011647067  0.001545298   -0.109746623
## pct_hh_pov           0.106858205 -0.018100029  0.014795814    0.011156172
## pct_poc              0.113823690  0.017142692 -0.008669098   -0.271775006
##                     pct_impervious mean_aadt_intensity   dist_m_tri  dist_m_npl
## mean_pm                 0.06114033         -0.03549398 -0.159193706 -0.13842663
## mean_o3                -0.04109912          0.01888934  0.056635532  0.05283628
## mean_temp               0.05562523          0.07182855 -0.053998558 -0.01089956
## pct_tree_cover          0.14164056          0.32971677 -0.009161339  0.04178106
## pct_impervious          1.00000000          0.50844411 -0.448678724 -0.17426369
## mean_aadt_intensity     0.50844411          1.00000000 -0.062619247  0.06152095
## dist_m_tri             -0.44867872         -0.06261925  1.000000000  0.50138396
## dist_m_npl             -0.17426369          0.06152095  0.501383960  1.00000000
## dist_m_waste_site      -0.15168685          0.10755964  0.412369055  0.54385239
## dist_m_major_emit       0.06211712          0.09495686  0.175965418  0.65505772
## dist_m_cafo             0.18326720          0.27696155  0.196849357  0.23859436
## dist_m_mine_well        0.02524829          0.12008641  0.184760224  0.03659688
## cvd_rate_adj            0.38371166          0.05527416 -0.426652406 -0.20525615
## res_rate_adj            0.40251263          0.12199419 -0.376750794 -0.17601130
## violent_crime_rate      0.31693831          0.11041575 -0.062519618 -0.03185242
## property_crime_rate     0.24673907          0.07479259 -0.058223492 -0.15232247
## pct_less_hs             0.33564418         -0.03883608 -0.379376300 -0.15916230
## pct_unemp               0.39291400          0.14739715 -0.198747643  0.13253691
## pct_limited_eng         0.38111402          0.03855846 -0.254907958  0.01801953
## pct_hh_pov              0.56509450          0.19888999 -0.315587892 -0.03111065
## pct_poc                 0.29005220          0.02408835 -0.307674381 -0.01906733
##                     dist_m_waste_site dist_m_major_emit  dist_m_cafo
## mean_pm                   -0.19023294       0.035715124 -0.303095664
## mean_o3                    0.03698459       0.059253499 -0.001691929
## mean_temp                  0.00554638       0.009628753  0.007701165
## pct_tree_cover             0.26833114       0.026770503  0.479321466
## pct_impervious            -0.15168685       0.062117120  0.183267205
## mean_aadt_intensity        0.10755964       0.094956864  0.276961553
## dist_m_tri                 0.41236906       0.175965418  0.196849357
## dist_m_npl                 0.54385239       0.655057717  0.238594356
## dist_m_waste_site          1.00000000       0.189779728  0.355027509
## dist_m_major_emit          0.18977973       1.000000000 -0.138307324
## dist_m_cafo                0.35502751      -0.138307324  1.000000000
## dist_m_mine_well           0.28275484      -0.270423318  0.652378929
## cvd_rate_adj              -0.41298787       0.113286594 -0.151743889
## res_rate_adj              -0.42432287      -0.012566704 -0.061257230
## violent_crime_rate        -0.25287368      -0.017896218  0.016755559
## property_crime_rate       -0.26866460      -0.209766780 -0.064647236
## pct_less_hs               -0.38800832       0.218931589 -0.300678627
## pct_unemp                 -0.12862329       0.330098571 -0.030506530
## pct_limited_eng           -0.22333346       0.355475551 -0.125707430
## pct_hh_pov                -0.30045944       0.249507656 -0.011486308
## pct_poc                   -0.16245202       0.311558055 -0.285584268
##                     dist_m_mine_well cvd_rate_adj res_rate_adj
## mean_pm                  -0.25751004  0.136954783  0.113962827
## mean_o3                  -0.05823036  0.006789463 -0.001793836
## mean_temp                -0.02118201  0.035699097  0.053237079
## pct_tree_cover            0.47797620 -0.176295758 -0.034307854
## pct_impervious            0.02524829  0.383711656  0.402512635
## mean_aadt_intensity       0.12008641  0.055274160  0.121994187
## dist_m_tri                0.18476022 -0.426652406 -0.376750794
## dist_m_npl                0.03659688 -0.205256148 -0.176011297
## dist_m_waste_site         0.28275484 -0.412987865 -0.424322872
## dist_m_major_emit        -0.27042332  0.113286594 -0.012566704
## dist_m_cafo               0.65237893 -0.151743889 -0.061257230
## dist_m_mine_well          1.00000000 -0.410752544 -0.234765650
## cvd_rate_adj             -0.41075254  1.000000000  0.864359590
## res_rate_adj             -0.23476565  0.864359590  1.000000000
## violent_crime_rate       -0.15245003  0.475234675  0.499449246
## property_crime_rate      -0.05640681  0.211613232  0.280786581
## pct_less_hs              -0.37449548  0.570813439  0.470409304
## pct_unemp                -0.27052616  0.468277441  0.441149256
## pct_limited_eng          -0.27607853  0.490577454  0.380164971
## pct_hh_pov               -0.21843600  0.538480631  0.557944498
## pct_poc                  -0.51797735  0.597594464  0.393598671
##                     violent_crime_rate property_crime_rate pct_less_hs
## mean_pm                     0.05873094         0.088879773  0.14204622
## mean_o3                     0.02977242        -0.025156291  0.01633882
## mean_temp                   0.03749739         0.037142591  0.01200908
## pct_tree_cover             -0.20552631        -0.201827442 -0.19081045
## pct_impervious              0.31693831         0.246739067  0.33564418
## mean_aadt_intensity         0.11041575         0.074792588 -0.03883608
## dist_m_tri                 -0.06251962        -0.058223492 -0.37937630
## dist_m_npl                 -0.03185242        -0.152322474 -0.15916230
## dist_m_waste_site          -0.25287368        -0.268664603 -0.38800832
## dist_m_major_emit          -0.01789622        -0.209766780  0.21893159
## dist_m_cafo                 0.01675556        -0.064647236 -0.30067863
## dist_m_mine_well           -0.15245003        -0.056406808 -0.37449548
## cvd_rate_adj                0.47523468         0.211613232  0.57081344
## res_rate_adj                0.49944925         0.280786581  0.47040930
## violent_crime_rate          1.00000000         0.705151942  0.27967307
## property_crime_rate         0.70515194         1.000000000 -0.00684836
## pct_less_hs                 0.27967307        -0.006848360  1.00000000
## pct_unemp                   0.35971778         0.007623781  0.62343462
## pct_limited_eng             0.24385889        -0.050184228  0.80738433
## pct_hh_pov                  0.42127121         0.163143151  0.72420883
## pct_poc                     0.31980337        -0.053765481  0.81887450
##                        pct_unemp pct_limited_eng  pct_hh_pov      pct_poc
## mean_pm              0.032317153     0.083396591  0.10685820  0.113823690
## mean_o3              0.018969666     0.011647067 -0.01810003  0.017142692
## mean_temp            0.011417056     0.001545298  0.01479581 -0.008669098
## pct_tree_cover      -0.021515177    -0.109746623  0.01115617 -0.271775006
## pct_impervious       0.392914001     0.381114020  0.56509450  0.290052202
## mean_aadt_intensity  0.147397153     0.038558463  0.19888999  0.024088345
## dist_m_tri          -0.198747643    -0.254907958 -0.31558789 -0.307674381
## dist_m_npl           0.132536906     0.018019533 -0.03111065 -0.019067333
## dist_m_waste_site   -0.128623290    -0.223333456 -0.30045944 -0.162452016
## dist_m_major_emit    0.330098571     0.355475551  0.24950766  0.311558055
## dist_m_cafo         -0.030506530    -0.125707430 -0.01148631 -0.285584268
## dist_m_mine_well    -0.270526163    -0.276078529 -0.21843600 -0.517977353
## cvd_rate_adj         0.468277441     0.490577454  0.53848063  0.597594464
## res_rate_adj         0.441149256     0.380164971  0.55794450  0.393598671
## violent_crime_rate   0.359717785     0.243858891  0.42127121  0.319803374
## property_crime_rate  0.007623781    -0.050184228  0.16314315 -0.053765481
## pct_less_hs          0.623434625     0.807384330  0.72420883  0.818874497
## pct_unemp            1.000000000     0.612939575  0.68048090  0.640031449
## pct_limited_eng      0.612939575     1.000000000  0.74208323  0.749164620
## pct_hh_pov           0.680480902     0.742083231  1.00000000  0.620401357
## pct_poc              0.640031449     0.749164620  0.62040136  1.000000000
ggplot(pivot_longer(as.data.frame(X.scaled), mean_pm:pct_poc, 
                    names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

1.2 Covariate data

Covariates were assessed at the individual level. These were selected based on previous HS studies and others in the literature and informed by a DAG.

W <- select(hs_data2, 
            lat, lon, lat_lon_int,
            ed_no_hs, ed_hs, ed_aa, ed_4yr,
            low_bmi, ovwt_bmi, obese_bmi,
            concep_spring, concep_summer, concep_fall,
            concep_2010, concep_2011, concep_2012, concep_2013,
            maternal_age, any_smoker, smokeSH, mean_cpss, mean_epsd,
            male, gest_age_w) %>%
  as.matrix()
head(W)
##           lat       lon lat_lon_int ed_no_hs ed_hs ed_aa ed_4yr low_bmi
## [1,] 39.79402 -104.8133   -4170.944        0     0     1      0       0
## [2,] 39.62671 -104.9927   -4160.517        0     0     1      0       0
## [3,] 39.74934 -104.9129   -4170.219        0     0     0      0       0
## [4,] 39.68397 -104.8933   -4162.583        0     0     1      0       0
## [5,] 39.79134 -104.7669   -4168.814        0     0     0      1       0
## [6,] 39.68050 -104.9451   -4164.274        0     0     1      0       0
##      ovwt_bmi obese_bmi concep_spring concep_summer concep_fall concep_2010
## [1,]        0         0             0             0           0           0
## [2,]        0         0             0             0           0           1
## [3,]        0         0             0             0           0           1
## [4,]        0         0             1             0           0           1
## [5,]        0         0             1             0           0           1
## [6,]        0         0             0             0           0           1
##      concep_2011 concep_2012 concep_2013 maternal_age any_smoker smokeSH
## [1,]           0           0           0           19          0       1
## [2,]           0           0           0           36          0       0
## [3,]           0           0           0           34          0       0
## [4,]           0           0           0           28          0       0
## [5,]           0           0           0           30          0       0
## [6,]           0           0           0           22          0       0
##      mean_cpss mean_epsd male gest_age_w
## [1,]        29         0    0   40.57143
## [2,]        19         2    1   35.85714
## [3,]        19         1    0   40.42857
## [4,]        20         0    0   36.28571
## [5,]        15         0    1   38.42857
## [6,]        17         1    0   40.71429

Scaled the non-binary (continuous) covariates

colnames(W)
##  [1] "lat"           "lon"           "lat_lon_int"   "ed_no_hs"     
##  [5] "ed_hs"         "ed_aa"         "ed_4yr"        "low_bmi"      
##  [9] "ovwt_bmi"      "obese_bmi"     "concep_spring" "concep_summer"
## [13] "concep_fall"   "concep_2010"   "concep_2011"   "concep_2012"  
## [17] "concep_2013"   "maternal_age"  "any_smoker"    "smokeSH"      
## [21] "mean_cpss"     "mean_epsd"     "male"          "gest_age_w"
W.s <- apply(W[,c(1, 2, 3, 18, 21, 22, 24)], 2, scale) #' just the continuous ones

W.scaled <- cbind(W.s[,1:3],
                  W[,4:17], W.s[,4],
                  W[,19:20], W.s[,5:6],
                  W[,23], W.s[,7])
colnames(W.scaled)
##  [1] "lat"           "lon"           "lat_lon_int"   "ed_no_hs"     
##  [5] "ed_hs"         "ed_aa"         "ed_4yr"        "low_bmi"      
##  [9] "ovwt_bmi"      "obese_bmi"     "concep_spring" "concep_summer"
## [13] "concep_fall"   "concep_2010"   "concep_2011"   "concep_2012"  
## [17] "concep_2013"   ""              "any_smoker"    "smokeSH"      
## [21] "mean_cpss"     "mean_epsd"     ""              ""
colnames(W.scaled) <- colnames(W)
head(W.scaled)
##             lat        lon lat_lon_int ed_no_hs ed_hs ed_aa ed_4yr low_bmi
## [1,]  0.9587536  0.5410850  -0.5821980        0     0     1      0       0
## [2,] -1.5498523 -1.6236392   0.6519093        0     0     1      0       0
## [3,]  0.2887793 -0.6606299  -0.4964164        0     0     0      0       0
## [4,] -0.6913627 -0.4239607   0.4073829        0     0     1      0       0
## [5,]  0.9185421  1.1019032  -0.3300513        0     0     0      1       0
## [6,] -0.7433125 -1.0489343   0.2071583        0     0     1      0       0
##      ovwt_bmi obese_bmi concep_spring concep_summer concep_fall concep_2010
## [1,]        0         0             0             0           0           0
## [2,]        0         0             0             0           0           1
## [3,]        0         0             0             0           0           1
## [4,]        0         0             1             0           0           1
## [5,]        0         0             1             0           0           1
## [6,]        0         0             0             0           0           1
##      concep_2011 concep_2012 concep_2013 maternal_age any_smoker smokeSH
## [1,]           0           0           0  -1.39815187          0       1
## [2,]           0           0           0   1.35109608          0       0
## [3,]           0           0           0   1.02765515          0       0
## [4,]           0           0           0   0.05733234          0       0
## [5,]           0           0           0   0.38077328          0       0
## [6,]           0           0           0  -0.91299047          0       0
##       mean_cpss  mean_epsd male gest_age_w
## [1,]  3.3147856 -1.2832098    0  0.7037686
## [2,]  0.1179652 -0.6860171    1 -1.9146645
## [3,]  0.1179652 -0.9846134    0  0.6244221
## [4,]  0.4376472 -1.2832098    0 -1.6766251
## [5,] -1.1607630 -1.2832098    1 -0.4864283
## [6,] -0.5213989 -0.9846134    0  0.7831150
summary(W.scaled)
##       lat                lon           lat_lon_int          ed_no_hs     
##  Min.   :-2.45418   Min.   :-2.5043   Min.   :-3.48430   Min.   :0.0000  
##  1st Qu.:-0.62577   1st Qu.:-0.5848   1st Qu.:-0.48738   1st Qu.:0.0000  
##  Median : 0.03151   Median : 0.1214   Median : 0.02121   Median :0.0000  
##  Mean   : 0.00000   Mean   : 0.0000   Mean   : 0.00000   Mean   :0.1527  
##  3rd Qu.: 0.42402   3rd Qu.: 0.6654   3rd Qu.: 0.60627   3rd Qu.:0.0000  
##  Max.   : 4.00304   Max.   : 4.5531   Max.   : 2.60273   Max.   :1.0000  
##      ed_hs            ed_aa            ed_4yr          low_bmi       
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.00000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000  
##  Median :0.0000   Median :0.0000   Median :0.0000   Median :0.00000  
##  Mean   :0.1851   Mean   :0.2319   Mean   :0.2185   Mean   :0.03344  
##  3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.00000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.00000  
##     ovwt_bmi       obese_bmi      concep_spring    concep_summer   
##  Min.   :0.000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.000   Median :0.0000   Median :0.0000   Median :0.0000  
##  Mean   :0.262   Mean   :0.1996   Mean   :0.2497   Mean   :0.2408  
##  3rd Qu.:1.000   3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.0000  
##  Max.   :1.000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##   concep_fall      concep_2010      concep_2011      concep_2012    
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.0000   Median :0.0000   Median :0.0000  
##  Mean   :0.2709   Mean   :0.1616   Mean   :0.3021   Mean   :0.2932  
##  3rd Qu.:1.0000   3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:1.0000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##   concep_2013      maternal_age        any_smoker         smokeSH      
##  Min.   :0.0000   Min.   :-1.88331   Min.   :0.00000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:-0.91299   1st Qu.:0.00000   1st Qu.:0.0000  
##  Median :0.0000   Median : 0.05733   Median :0.00000   Median :0.0000  
##  Mean   :0.2419   Mean   : 0.00000   Mean   :0.08696   Mean   :0.2575  
##  3rd Qu.:0.0000   3rd Qu.: 0.70421   3rd Qu.:0.00000   3rd Qu.:1.0000  
##  Max.   :1.0000   Max.   : 2.64486   Max.   :1.00000   Max.   :1.0000  
##    mean_cpss         mean_epsd            male          gest_age_w     
##  Min.   :-5.9560   Min.   :-1.2832   Min.   :0.0000   Min.   :-7.7070  
##  1st Qu.:-0.5214   1st Qu.:-0.7855   1st Qu.:0.0000   1st Qu.:-0.3277  
##  Median : 0.0114   Median :-0.1884   Median :1.0000   Median : 0.1483  
##  Mean   : 0.0000   Mean   : 0.0000   Mean   :0.5117   Mean   : 0.0000  
##  3rd Qu.: 0.5442   3rd Qu.: 0.6079   3rd Qu.:1.0000   3rd Qu.: 0.6244  
##  Max.   : 4.5935   Max.   : 6.0324   Max.   :1.0000   Max.   : 2.9255

Variance and histograms for the scaled covariates

var(W.scaled)
##                        lat            lon  lat_lon_int      ed_no_hs
## lat            1.000000000 -0.25261855699 -0.926170284  0.0058668471
## lon           -0.252618557  1.00000000000  0.598841550  0.0173291290
## lat_lon_int   -0.926170284  0.59884155012  1.000000000  0.0019047436
## ed_no_hs       0.005866847  0.01732912905  0.001904744  0.1295488931
## ed_hs         -0.013065279  0.04117136599  0.026869409 -0.0282962056
## ed_aa         -0.007178943  0.04676104709  0.024182422 -0.0354554865
## ed_4yr         0.002235236 -0.00766878563 -0.004860779 -0.0334099777
## low_bmi       -0.002977458 -0.00003551643  0.002453115 -0.0039977007
## ovwt_bmi       0.020588007  0.00512460048 -0.015060264  0.0045849757
## obese_bmi      0.016566934  0.00976713009 -0.009896473  0.0063181836
## concep_spring  0.014329290 -0.00046075172 -0.012039363 -0.0002364031
## concep_summer -0.014031905 -0.00711327850  0.008844405 -0.0044530877
## concep_fall    0.005490559  0.01642183233  0.001845775  0.0110338032
## concep_2010    0.011068124  0.00844610317 -0.005886105 -0.0001629937
## concep_2011   -0.022063544  0.01869831001  0.025541096  0.0096091635
## concep_2012    0.002443596 -0.00706763788 -0.004770794 -0.0035360925
## concep_2013    0.007481786 -0.02068066481 -0.014234422 -0.0057396182
## maternal_age   0.030778940 -0.17980907079 -0.095594562 -0.1376124653
## any_smoker    -0.008227433  0.02279799333  0.015696371  0.0179541925
## smokeSH       -0.011104226  0.04668855425  0.027384613  0.0309364548
## mean_cpss     -0.025836085 -0.01114736129  0.017046231 -0.0561153540
## mean_epsd     -0.034737548  0.05084465609  0.048585549  0.0670107276
## male           0.029004763 -0.02552947737 -0.033951919 -0.0135085702
## gest_age_w     0.011119160 -0.03926647196 -0.024532454 -0.0076928484
##                        ed_hs        ed_aa        ed_4yr        low_bmi
## lat           -0.01306527915 -0.007178943  0.0022352364 -0.00297745845
## lon            0.04117136599  0.046761047 -0.0076687856 -0.00003551643
## lat_lon_int    0.02686940852  0.024182422 -0.0048607788  0.00245311454
## ed_no_hs      -0.02829620561 -0.035455487 -0.0334099777 -0.00399770067
## ed_hs          0.15098194378 -0.042960663 -0.0404821628 -0.00173196369
## ed_aa         -0.04296066253  0.178312629 -0.0507246377  0.00786102484
## ed_4yr        -0.04048216276 -0.050724638  0.1709517837 -0.00173569637
## low_bmi       -0.00173196369  0.007861025 -0.0017356964  0.03236233875
## ovwt_bmi      -0.00612657270  0.015075052  0.0040748427 -0.00877179885
## obese_bmi      0.02441297380  0.009478520 -0.0124024526 -0.00668149785
## concep_spring  0.00395788541  0.006761128 -0.0066354615 -0.00501298973
## concep_summer -0.00331835284 -0.011257764  0.0064762004  0.00309812470
## concep_fall    0.00226573698 -0.007084627  0.0010078237  0.00320637243
## concep_2010    0.00576574693  0.004884834  0.0003533604  0.00128404204
## concep_2011   -0.00463350056  0.002410067  0.0053402214  0.00439336479
## concep_2012    0.00371526119 -0.005564182 -0.0061016882 -0.00535266364
## concep_2013   -0.00464096592 -0.002587992  0.0006519748 -0.00028741639
## maternal_age  -0.10868310364 -0.040296710  0.1091044519 -0.01089529356
## any_smoker     0.00174689441  0.011063665 -0.0156735248  0.00155279503
## smokeSH        0.02483352246  0.022806677 -0.0362443263  0.00142215122
## mean_cpss     -0.03433895561  0.030714793  0.0282429323  0.00484169668
## mean_epsd      0.02014619096  0.025424770 -0.0463684315  0.00946748435
## male           0.00006345557  0.000630823  0.0063679527 -0.00262407430
## gest_age_w    -0.01723767893 -0.035168407  0.0301476493 -0.00601412877
##                    ovwt_bmi     obese_bmi concep_spring  concep_summer
## lat            0.0205880066  0.0165669344  0.0143292896 -0.01403190526
## lon            0.0051246005  0.0097671301 -0.0004607517 -0.00711327850
## lat_lon_int   -0.0150602639 -0.0098964732 -0.0120393632  0.00884440451
## ed_no_hs       0.0045849757  0.0063181836 -0.0002364031 -0.00445308767
## ed_hs         -0.0061265727  0.0244129738  0.0039578854 -0.00331835284
## ed_aa          0.0150750518  0.0094785197  0.0067611284 -0.01125776398
## ed_4yr         0.0040748427 -0.0124024526 -0.0066354615  0.00647620043
## low_bmi       -0.0087717989 -0.0066814978 -0.0050129897  0.00309812470
## ovwt_bmi       0.1935643614 -0.0523383998  0.0092806876 -0.00512123746
## obese_bmi     -0.0523383998  0.1599105152 -0.0085938744 -0.00346392738
## concep_spring  0.0092806876 -0.0085938744  0.1875696767 -0.06020066890
## concep_summer -0.0051212375 -0.0034639274 -0.0602006689  0.18302078356
## concep_fall    0.0026091436  0.0005673674 -0.0677257525 -0.06530697563
## concep_2010   -0.0033345278 -0.0043921206 -0.0236714146  0.00009331701
## concep_2011    0.0055828456  0.0032598742  0.0003633142 -0.00140348782
## concep_2012   -0.0043547938  0.0072737498 -0.0085677457  0.00186260750
## concep_2013    0.0023988692 -0.0059187868  0.0321545529 -0.00028368371
## maternal_age   0.0089002276  0.0027900741 -0.0149065532  0.01490413862
## any_smoker    -0.0060656056  0.0027173913  0.0016983696  0.00024262422
## smokeSH       -0.0106232083  0.0110524666 -0.0041134138 -0.00627836837
## mean_cpss     -0.0082476896 -0.0087226114  0.0079650833  0.01166899615
## mean_epsd     -0.0019127169  0.0281330380 -0.0063209443 -0.01563660013
## male           0.0008361204 -0.0017804885 -0.0062746357 -0.00393797778
## gest_age_w    -0.0148466585 -0.0214614301 -0.0179961830  0.01920131892
##                 concep_fall    concep_2010   concep_2011  concep_2012
## lat            0.0054905592  0.01106812411 -0.0220635440  0.002443596
## lon            0.0164218323  0.00844610317  0.0186983100 -0.007067638
## lat_lon_int    0.0018457750 -0.00588610547  0.0255410960 -0.004770794
## ed_no_hs       0.0110338032 -0.00016299371  0.0096091635 -0.003536093
## ed_hs          0.0022657370  0.00576574693 -0.0046335006  0.003715261
## ed_aa         -0.0070846273  0.00488483437  0.0024100673 -0.005564182
## ed_4yr         0.0010078237  0.00035336041  0.0053402214 -0.006101688
## low_bmi        0.0032063724  0.00128404204  0.0043933648 -0.005352664
## ovwt_bmi       0.0026091436 -0.00333452779  0.0055828456 -0.004354794
## obese_bmi      0.0005673674 -0.00439212056  0.0032598742  0.007273750
## concep_spring -0.0677257525 -0.02367141464  0.0003633142 -0.008567746
## concep_summer -0.0653069756  0.00009331701 -0.0014034878  0.001862608
## concep_fall    0.1977350096  0.02870431199 -0.0127396381  0.001955925
## concep_2010    0.0287043120  0.13567048893 -0.0488918916 -0.047448589
## concep_2011   -0.0127396381 -0.04889189162  0.2110780976 -0.088679776
## concep_2012    0.0019559245 -0.04744858855 -0.0886797758  0.207464863
## concep_2013   -0.0176182513 -0.03914959588 -0.0731692447 -0.071009267
## maternal_age  -0.0196470231 -0.02663971411 -0.0380704459  0.031448396
## any_smoker    -0.0023777174  0.00266886646  0.0105298913 -0.011015140
## smokeSH       -0.0028778966  0.00631569517  0.0136280160 -0.018670867
## mean_cpss     -0.0055888831  0.00832724099 -0.0113573536 -0.011161856
## mean_epsd      0.0265650931 -0.01748485806  0.0347867417 -0.022850868
## male           0.0018476768  0.00089584329 -0.0029824116 -0.001761825
## gest_age_w     0.0141959621  0.01072301448 -0.0118973482 -0.026416733
##                 concep_2013 maternal_age    any_smoker      smokeSH
## lat            0.0074817863  0.030778940 -0.0082274331 -0.011104226
## lon           -0.0206806648 -0.179809071  0.0227979933  0.046688554
## lat_lon_int   -0.0142344221 -0.095594562  0.0156963705  0.027384613
## ed_no_hs      -0.0057396182 -0.137612465  0.0179541925  0.030936455
## ed_hs         -0.0046409659 -0.108683104  0.0017468944  0.024833522
## ed_aa         -0.0025879917 -0.040296710  0.0110636646  0.022806677
## ed_4yr         0.0006519748  0.109104452 -0.0156735248 -0.036244326
## low_bmi       -0.0002874164 -0.010895294  0.0015527950  0.001422151
## ovwt_bmi       0.0023988692  0.008900228 -0.0060656056 -0.010623208
## obese_bmi     -0.0059187868  0.002790074  0.0027173913  0.011052467
## concep_spring  0.0321545529 -0.014906553  0.0016983696 -0.004113414
## concep_summer -0.0002836837  0.014904139  0.0002426242 -0.006278368
## concep_fall   -0.0176182513 -0.019647023 -0.0023777174 -0.002877897
## concep_2010   -0.0391495959 -0.026639714  0.0026688665  0.006315695
## concep_2011   -0.0731692447 -0.038070446  0.0105298913  0.013628016
## concep_2012   -0.0710092670  0.031448396 -0.0110151398 -0.018670867
## concep_2013    0.1835981048  0.034822201 -0.0020865683 -0.002101499
## maternal_age   0.0348222009  1.000000000 -0.0466296108 -0.155964054
## any_smoker    -0.0020865683 -0.046629611  0.0794836957  0.049010093
## smokeSH       -0.0021014990 -0.155964054  0.0490100932  0.191419314
## mean_cpss      0.0104924310  0.100637638  0.0176429080  0.031721118
## mean_epsd      0.0069811381 -0.160410684  0.0421446647  0.108180210
## male           0.0044194935  0.023413804  0.0023291925  0.002004449
## gest_age_w     0.0268056111  0.091663607 -0.0149814181 -0.050311537
##                  mean_cpss    mean_epsd           male   gest_age_w
## lat           -0.025836085 -0.034737548  0.02900476291  0.011119160
## lon           -0.011147361  0.050844656 -0.02552947737 -0.039266472
## lat_lon_int    0.017046231  0.048585549 -0.03395191918 -0.024532454
## ed_no_hs      -0.056115354  0.067010728 -0.01350857023 -0.007692848
## ed_hs         -0.034338956  0.020146191  0.00006345557 -0.017237679
## ed_aa          0.030714793  0.025424770  0.00063082298 -0.035168407
## ed_4yr         0.028242932 -0.046368432  0.00636795270  0.030147649
## low_bmi        0.004841697  0.009467484 -0.00262407430 -0.006014129
## ovwt_bmi      -0.008247690 -0.001912717  0.00083612040 -0.014846658
## obese_bmi     -0.008722611  0.028133038 -0.00178048853 -0.021461430
## concep_spring  0.007965083 -0.006320944 -0.00627463569 -0.017996183
## concep_summer  0.011668996 -0.015636600 -0.00393797778  0.019201319
## concep_fall   -0.005588883  0.026565093  0.00184767678  0.014195962
## concep_2010    0.008327241 -0.017484858  0.00089584329  0.010723014
## concep_2011   -0.011357354  0.034786742 -0.00298241161 -0.011897348
## concep_2012   -0.011161856 -0.022850868 -0.00176182513 -0.026416733
## concep_2013    0.010492431  0.006981138  0.00441949355  0.026805611
## maternal_age   0.100637638 -0.160410684  0.02341380415  0.091663607
## any_smoker     0.017642908  0.042144665  0.00232919255 -0.014981418
## smokeSH        0.031721118  0.108180210  0.00200444935 -0.050311537
## mean_cpss      1.000000000  0.455187203 -0.00331530432 -0.037142336
## mean_epsd      0.455187203  1.000000000  0.00154181454 -0.137187808
## male          -0.003315304  0.001541815  0.25014184185 -0.007427180
## gest_age_w    -0.037142336 -0.137187808 -0.00742717951  1.000000000
ggplot(pivot_longer(as.data.frame(W.scaled), lat:gest_age_w, 
                    names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

1.3 Response data: birth weight (in grams)

Y <- select(hs_data2, birth_weight) %>%
  as.matrix()
head(Y)
##      birth_weight
## [1,]         2860
## [2,]         2755
## [3,]         3505
## [4,]         2695
## [5,]         3355
## [6,]         3810

Distribution of birth weight and scaled birth weight

hist(Y, breaks = 20)

hist(scale(Y), breaks = 20)

Dropping gest_age_w from the covariates

colnames(W.scaled)
##  [1] "lat"           "lon"           "lat_lon_int"   "ed_no_hs"     
##  [5] "ed_hs"         "ed_aa"         "ed_4yr"        "low_bmi"      
##  [9] "ovwt_bmi"      "obese_bmi"     "concep_spring" "concep_summer"
## [13] "concep_fall"   "concep_2010"   "concep_2011"   "concep_2012"  
## [17] "concep_2013"   "maternal_age"  "any_smoker"    "smokeSH"      
## [21] "mean_cpss"     "mean_epsd"     "male"          "gest_age_w"
W.scaled2 <- W.scaled[,-c(ncol(W.scaled))]
colnames(W.scaled2)
##  [1] "lat"           "lon"           "lat_lon_int"   "ed_no_hs"     
##  [5] "ed_hs"         "ed_aa"         "ed_4yr"        "low_bmi"      
##  [9] "ovwt_bmi"      "obese_bmi"     "concep_spring" "concep_summer"
## [13] "concep_fall"   "concep_2010"   "concep_2011"   "concep_2012"  
## [17] "concep_2013"   "maternal_age"  "any_smoker"    "smokeSH"      
## [21] "mean_cpss"     "mean_epsd"     "male"

2 RIDGE regression

To see if there might be something going on, Lauren suggested a ridge regression with a small penalty.

set.seed(123)

library(glmnet)
## Loading required package: Matrix
## 
## Attaching package: 'Matrix'
## The following objects are masked from 'package:tidyr':
## 
##     expand, pack, unpack
## Loaded glmnet 4.0-2
lambda_seq <- 10^seq(4, -4, by = -.05)

#' Best lambda from CV
ridge_cv <- cv.glmnet(X, Y, alpha = 0, lambda = lambda_seq,
                      standardize = T, standardize.response = T)
plot(ridge_cv)

best_lambda <- ridge_cv$lambda.min
best_lambda
## [1] 891.2509
#' Fit the model using the best_lambda
bw_ridge <- glmnet(X, Y, alpha = 0, lambda = best_lambda,
                   standardize = T, standardize.response = T)
summary(bw_ridge)
##           Length Class     Mode   
## a0         1     -none-    numeric
## beta      21     dgCMatrix S4     
## df         1     -none-    numeric
## dim        2     -none-    numeric
## lambda     1     -none-    numeric
## dev.ratio  1     -none-    numeric
## nulldev    1     -none-    numeric
## npasses    1     -none-    numeric
## jerr       1     -none-    numeric
## offset     1     -none-    logical
## call       7     -none-    call   
## nobs       1     -none-    numeric

Ridge regression coefficients

coef(bw_ridge)
## 22 x 1 sparse Matrix of class "dgCMatrix"
##                                  s0
## (Intercept)         3756.2244127611
## mean_pm                6.5831658736
## mean_o3               -5.7909309972
## mean_temp             -2.6190406717
## pct_tree_cover         0.0346391254
## pct_impervious        -0.4281346032
## mean_aadt_intensity   -0.0002915500
## dist_m_tri            -0.0003520682
## dist_m_npl             0.0001168135
## dist_m_waste_site      0.0017447014
## dist_m_major_emit     -0.0003705192
## dist_m_cafo           -0.0003121004
## dist_m_mine_well      -0.0022906005
## cvd_rate_adj          -0.1469368176
## res_rate_adj          -0.1446242346
## violent_crime_rate    -0.4156388202
## property_crime_rate   -0.0143345439
## pct_less_hs           -0.6736508410
## pct_unemp             -3.6551596165
## pct_limited_eng       -0.5218862220
## pct_hh_pov            -0.4758794734
## pct_poc               -0.4466466437

Ridge regression predictions

ridge_pred <- predict(bw_ridge, newx = X)
plot(Y, ridge_pred)

actual <- Y
preds <- ridge_pred
rsq <- 1 - (sum((preds - actual) ^ 2))/(sum((actual - mean(actual)) ^ 2))

The R2 value for this model is 0.03. Based on these results, it doesn’t look like there’s much here.

3 Nonparametric Bayesian Shrinkage (NPB): Birth weight

3.1 Finding the NPB priors

3.1.1 Vignette Priors

set.seed(123)

priors.npb.1 <- list(alpha.pi = 1, beta.pi = 1, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 1)

fit.npb.1 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.1, interact = F)
npb.sum.1 <- summary(fit.npb.1)
npb.sum.1$main.effects
##       Posterior Mean         SD 95% CI Lower 95% CI Upper   PIP
##  [1,]    -0.05907077  1.7292064     0.000000            0 0.008
##  [2,]    -1.18173936  6.7453018   -22.846654            0 0.050
##  [3,]    -0.68874315  5.1022188    -3.829552            0 0.032
##  [4,]    -0.09836726  1.3523591     0.000000            0 0.014
##  [5,]    -0.58334088  4.2590450    -2.025017            0 0.028
##  [6,]    -0.02810779  1.3627030     0.000000            0 0.018
##  [7,]    -0.07241864  1.6862869     0.000000            0 0.010
##  [8,]     0.12843949  1.6692407     0.000000            0 0.016
##  [9,]     0.29614136  3.3791200     0.000000            0 0.020
## [10,]    -0.04574610  1.1661326     0.000000            0 0.010
## [11,]    -1.02549044 12.1015196   -21.361864            0 0.048
## [12,]    -0.76889738  5.1972449    -7.703709            0 0.032
## [13,]    -0.50082159  4.2854699    -1.645144            0 0.028
## [14,]    -0.52647452  4.1378266     0.000000            0 0.020
## [15,]    -0.14443889  1.7466026     0.000000            0 0.018
## [16,]    -0.03206135  0.8482502     0.000000            0 0.012
## [17,]    -0.71146302  4.8104069    -9.104986            0 0.032
## [18,]    -6.57484938 17.6038554   -65.994065            0 0.150
## [19,]    -0.32089031  3.4509916     0.000000            0 0.016
## [20,]    -0.21027072  2.1926996     0.000000            0 0.016
## [21,]    -0.63622272  5.4262819     0.000000            0 0.026
plot(fit.npb.1$beta[,1], type = "l")

plot(fit.npb.1$beta[,2], type = "l")

plot(fit.npb.1$beta[,13], type = "l")

3.1.2 Try making a.phi1 = 10 and sig2inv.mu1 = 10

priors.npb.24 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 10, sig2inv.mu1 = 10)

fit.npb.24 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.24, interact = F)
npb.sum.24 <- summary(fit.npb.24)
npb.sum.24$main.effects
##       Posterior Mean        SD 95% CI Lower 95% CI Upper   PIP
##  [1,]    -0.37835158  6.444211    -12.39843    15.459027 0.254
##  [2,]    -6.50866456 13.285146    -47.61147     5.157978 0.422
##  [3,]    -2.99829637  9.530987    -27.10395     9.170820 0.316
##  [4,]    -1.83469729  7.302263    -20.66994     8.664141 0.302
##  [5,]    -4.15010395  8.878299    -31.18568     1.432763 0.364
##  [6,]    -1.13456265  5.999765    -13.20965     9.648707 0.262
##  [7,]    -1.06393850  6.067273    -14.88747    10.146850 0.274
##  [8,]    -0.41269500  6.179682    -13.50993    11.850908 0.238
##  [9,]     0.08388743  7.009746    -12.23644    21.113180 0.262
## [10,]    -0.45998103  6.272873    -11.69475    11.850908 0.238
## [11,]    -2.86724980 11.352373    -33.00612     8.125983 0.348
## [12,]    -3.68104712  8.584663    -26.86129     3.369650 0.354
## [13,]    -3.81491402  8.769486    -30.58368     3.211650 0.382
## [14,]    -3.48433858  7.905814    -25.16353     3.591160 0.354
## [15,]    -1.13941047  5.331153    -14.58868     4.475193 0.232
## [16,]    -2.06055760  6.610397    -19.45050     7.383645 0.310
## [17,]    -2.67440654  7.648666    -25.96178     7.642657 0.336
## [18,]   -17.54869944 23.031327    -74.98278     0.000000 0.664
## [19,]    -2.39876713  6.867868    -19.15311     7.383645 0.338
## [20,]    -2.19811559  7.659921    -22.28194     8.860543 0.332
## [21,]    -2.38098284  7.546698    -22.00851     9.174345 0.372
plot(fit.npb.24$beta[,1], type = "l")

plot(fit.npb.24$beta[,2], type = "l")

plot(fit.npb.24$beta[,13], type = "l")

3.2 Fit the NPB model without temperature

Below I’ve used the set of priors labeled “24” and set scaleY = T

The priors are as follows: r priors.npb.24

Note that this version of the model does not include gest_age_w. It does include an indicator variable for season of conception (ref = winter) and the lon/lat as covariates and the percentage of the census tract population that is not NHW as an exposure.

priors.npb <- priors.npb.24

#' Exposures (minus temperature)
colnames(X.scaled)
##  [1] "mean_pm"             "mean_o3"             "mean_temp"          
##  [4] "pct_tree_cover"      "pct_impervious"      "mean_aadt_intensity"
##  [7] "dist_m_tri"          "dist_m_npl"          "dist_m_waste_site"  
## [10] "dist_m_major_emit"   "dist_m_cafo"         "dist_m_mine_well"   
## [13] "cvd_rate_adj"        "res_rate_adj"        "violent_crime_rate" 
## [16] "property_crime_rate" "pct_less_hs"         "pct_unemp"          
## [19] "pct_limited_eng"     "pct_hh_pov"          "pct_poc"
#' Covariates
colnames(W.scaled2)
##  [1] "lat"           "lon"           "lat_lon_int"   "ed_no_hs"     
##  [5] "ed_hs"         "ed_aa"         "ed_4yr"        "low_bmi"      
##  [9] "ovwt_bmi"      "obese_bmi"     "concep_spring" "concep_summer"
## [13] "concep_fall"   "concep_2010"   "concep_2011"   "concep_2012"  
## [17] "concep_2013"   "maternal_age"  "any_smoker"    "smokeSH"      
## [21] "mean_cpss"     "mean_epsd"     "male"
# fit.npb <- npb(niter = 5000, nburn = 2500, X = X.scaled[,-c(3)], Y = Y, W = W.scaled2,
#                scaleY = TRUE,
#                priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb, file = here::here("Results", "NPB_Birth_Weight_v4a.1.rdata"))

load(here::here("Results", "NPB_Birth_Weight_v4a.1.rdata"))
npb.sum <- summary(fit.npb)

3.2.1 First, main effect regression coefficients with PIPs

rownames(npb.sum$main.effects) <- colnames(X.scaled[,-c(3)])
npb.sum$main.effects
##                     Posterior Mean        SD 95% CI Lower 95% CI Upper    PIP
## mean_pm                -0.64125098  5.911603   -15.455836    10.490517 0.1816
## mean_o3              -126.48202072 96.518824  -285.016660     3.445415 0.8044
## pct_tree_cover         -0.68083059  5.615548   -15.848685    10.739415 0.1900
## pct_impervious         -2.83488760  8.796487   -29.792364     5.146130 0.2520
## mean_aadt_intensity    -0.18793856  4.988127   -11.993448    10.921741 0.1692
## dist_m_tri             -0.76891442  6.081892   -17.209786    10.305810 0.1928
## dist_m_npl              0.34958475  5.844586   -10.729199    14.822900 0.1804
## dist_m_waste_site       1.45511736  8.095672    -9.515091    26.912081 0.1968
## dist_m_major_emit      -0.08282941  5.378265   -12.159189    12.434891 0.1872
## dist_m_cafo            -4.47615039 22.150639   -62.347984    14.992358 0.2892
## dist_m_mine_well       -2.67188258  9.303658   -32.030285     6.776363 0.2448
## cvd_rate_adj           -2.62833089  8.514285   -29.765889     4.970325 0.2524
## res_rate_adj           -3.01604247  9.570154   -32.440411     6.576391 0.2644
## violent_crime_rate     -0.14945003  5.737088   -12.685065    11.958291 0.1824
## property_crime_rate    -0.77234125  5.314391   -15.612152     8.053212 0.1860
## pct_less_hs            -1.42774630  7.154552   -22.018857     8.044627 0.2156
## pct_unemp             -23.79952093 28.421158   -87.511759     0.000000 0.6100
## pct_limited_eng        -1.34682390  6.381113   -18.977246     7.841900 0.2012
## pct_hh_pov             -1.24705339  7.810668   -22.139205    10.796265 0.2196
## pct_poc                -1.54490752  8.140743   -22.840185    10.342720 0.2308

3.2.3 Interactions

Next, all of the interactions between exposures or between exposures and covariates

npb.sum$interactions
##          Posterior Mean            SD 95% CI Lower 95% CI Upper    PIP
##   [1,]   0.017438215244   0.908986942       0.0000       0.0000 0.0012
##   [2,]  -0.001570933914   0.321889805       0.0000       0.0000 0.0012
##   [3,]  -0.005050155089   0.269284590       0.0000       0.0000 0.0008
##   [4,]  -0.000899881214   0.044994061       0.0000       0.0000 0.0004
##   [5,]   0.001401134043   0.070056702       0.0000       0.0000 0.0004
##   [6,]   0.006066131113   0.487992896       0.0000       0.0000 0.0020
##   [7,]  -0.002022843832   0.207040988       0.0000       0.0000 0.0008
##   [8,]  -0.003443891433   0.172194572       0.0000       0.0000 0.0004
##   [9,]  -0.012746513228   0.380095974       0.0000       0.0000 0.0016
##  [10,]  -0.012954477025   0.447726805       0.0000       0.0000 0.0012
##  [11,]  -0.007529079003   0.499802518       0.0000       0.0000 0.0020
##  [12,]   0.004234366871   0.174822849       0.0000       0.0000 0.0008
##  [13,]  -0.000522542019   0.018663667       0.0000       0.0000 0.0008
##  [14,]   0.002684209813   0.491394168       0.0000       0.0000 0.0016
##  [15,]  -0.002685413318   0.102346907       0.0000       0.0000 0.0008
##  [16,]   0.003675129802   0.135131564       0.0000       0.0000 0.0008
##  [17,]  -0.021002092163   0.971540034       0.0000       0.0000 0.0012
##  [18,]   0.010293649736   0.436031850       0.0000       0.0000 0.0008
##  [19,]  -0.003677054422   0.141189576       0.0000       0.0000 0.0008
##  [20,]  -0.013623634880   0.482453807       0.0000       0.0000 0.0020
##  [21,]   0.036604048143   1.049742933       0.0000       0.0000 0.0016
##  [22,]   0.001930581325   0.255933120       0.0000       0.0000 0.0008
##  [23,]  -0.030685262257   0.822218098       0.0000       0.0000 0.0020
##  [24,]  -0.013674663074   0.357493419       0.0000       0.0000 0.0016
##  [25,]  -0.141133047815   2.354546508       0.0000       0.0000 0.0052
##  [26,]  -0.003309136283   0.165456814       0.0000       0.0000 0.0004
##  [27,]  -0.028698613744   0.651846047       0.0000       0.0000 0.0024
##  [28,]  -0.034095865812   1.111646012       0.0000       0.0000 0.0028
##  [29,]   0.038558280507   0.945839927       0.0000       0.0000 0.0024
##  [30,]   0.013187448905   0.494270520       0.0000       0.0000 0.0008
##  [31,]   0.002061426957   0.088300307       0.0000       0.0000 0.0008
##  [32,]   0.008884293401   0.346748418       0.0000       0.0000 0.0008
##  [33,]   0.030184723995   0.751461394       0.0000       0.0000 0.0020
##  [34,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
##  [35,]   0.019378288894   0.670021652       0.0000       0.0000 0.0028
##  [36,]   0.063925069453   1.360714110       0.0000       0.0000 0.0036
##  [37,]   0.021393793579   0.682264400       0.0000       0.0000 0.0028
##  [38,]   0.002900487682   0.096687970       0.0000       0.0000 0.0012
##  [39,]   0.015651515844   0.667336857       0.0000       0.0000 0.0016
##  [40,]  -0.001722185300   0.094162569       0.0000       0.0000 0.0008
##  [41,]  -0.003541780846   0.136011195       0.0000       0.0000 0.0008
##  [42,]   0.005475479185   0.499829125       0.0000       0.0000 0.0020
##  [43,]   0.030142390523   0.722553361       0.0000       0.0000 0.0020
##  [44,]   0.002789029287   0.099781478       0.0000       0.0000 0.0012
##  [45,]  -0.002437755210   0.121887761       0.0000       0.0000 0.0004
##  [46,]  -0.000801669675   0.040083484       0.0000       0.0000 0.0004
##  [47,]  -0.006382014486   0.260635899       0.0000       0.0000 0.0012
##  [48,]   0.010828678000   0.541433900       0.0000       0.0000 0.0004
##  [49,]   0.002686972087   0.218579734       0.0000       0.0000 0.0016
##  [50,]   0.003542899605   0.464777891       0.0000       0.0000 0.0008
##  [51,]  -0.003736220736   0.327130735       0.0000       0.0000 0.0008
##  [52,]   0.008821398656   0.396972566       0.0000       0.0000 0.0020
##  [53,]   0.009041886699   0.396755945       0.0000       0.0000 0.0020
##  [54,]  -0.000577944101   0.058158836       0.0000       0.0000 0.0008
##  [55,]   0.026971400695   0.843952453       0.0000       0.0000 0.0024
##  [56,]  -0.001019368600   0.050968430       0.0000       0.0000 0.0004
##  [57,]   0.001614843671   0.080742184       0.0000       0.0000 0.0004
##  [58,]   0.000865437314   0.188763078       0.0000       0.0000 0.0016
##  [59,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
##  [60,]   0.002769339507   0.253434481       0.0000       0.0000 0.0016
##  [61,]   0.021860360388   0.716468177       0.0000       0.0000 0.0012
##  [62,]  -0.016926118032   0.505127268       0.0000       0.0000 0.0020
##  [63,]   0.002972905455   0.406784684       0.0000       0.0000 0.0020
##  [64,]   0.005252995207   0.219073175       0.0000       0.0000 0.0008
##  [65,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
##  [66,]   0.006878771304   0.280834028       0.0000       0.0000 0.0012
##  [67,]   0.004452993572   0.222649679       0.0000       0.0000 0.0004
##  [68,]  -0.001826710732   0.253277102       0.0000       0.0000 0.0016
##  [69,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
##  [70,]   0.002611424949   0.453651983       0.0000       0.0000 0.0020
##  [71,]   0.027548311537   0.980663046       0.0000       0.0000 0.0008
##  [72,]  -0.002432269265   0.121613463       0.0000       0.0000 0.0004
##  [73,]   0.002859903666   0.318165143       0.0000       0.0000 0.0020
##  [74,]   0.048423245606   1.357290016       0.0000       0.0000 0.0020
##  [75,]  -0.028597537829   0.604384190       0.0000       0.0000 0.0032
##  [76,]  -0.002492106568   0.283326689       0.0000       0.0000 0.0012
##  [77,]  -0.007137469416   0.279235206       0.0000       0.0000 0.0008
##  [78,]  -0.001876829422   0.093841471       0.0000       0.0000 0.0004
##  [79,]  -0.003443891433   0.172194572       0.0000       0.0000 0.0004
##  [80,]  -0.036243622373   0.772921544       0.0000       0.0000 0.0028
##  [81,]  -0.002844793467   0.356644753       0.0000       0.0000 0.0016
##  [82,]  -0.005578423578   0.412054185       0.0000       0.0000 0.0012
##  [83,]   0.030114973279   0.972608070       0.0000       0.0000 0.0020
##  [84,]   0.009590149377   0.305106295       0.0000       0.0000 0.0012
##  [85,]   0.012997012943   0.481661109       0.0000       0.0000 0.0008
##  [86,]   0.000147815230   0.321400840       0.0000       0.0000 0.0012
##  [87,]  -0.001883743643   0.094187182       0.0000       0.0000 0.0004
##  [88,]  -0.002745858685   0.126610039       0.0000       0.0000 0.0008
##  [89,]  -0.003309136283   0.165456814       0.0000       0.0000 0.0004
##  [90,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
##  [91,]   0.006476974448   0.381114713       0.0000       0.0000 0.0008
##  [92,]   0.020689470593   0.630132681       0.0000       0.0000 0.0024
##  [93,]   0.010863718653   0.726125306       0.0000       0.0000 0.0016
##  [94,]   0.000839967348   0.041998367       0.0000       0.0000 0.0004
##  [95,]  -0.005232153085   0.286351438       0.0000       0.0000 0.0012
##  [96,]   0.015907298158   0.961035297       0.0000       0.0000 0.0024
##  [97,]  -0.008616536394   0.311938475       0.0000       0.0000 0.0008
##  [98,]  -0.007338413467   0.366920673       0.0000       0.0000 0.0004
##  [99,]   0.000600569115   0.030028456       0.0000       0.0000 0.0004
## [100,]   0.011190121886   0.545506238       0.0000       0.0000 0.0012
## [101,]  -0.000330572739   0.064271480       0.0000       0.0000 0.0008
## [102,]   0.007485224916   0.781015773       0.0000       0.0000 0.0012
## [103,]   0.003417262854   0.430186987       0.0000       0.0000 0.0008
## [104,]  -0.009298867966   0.302529061       0.0000       0.0000 0.0012
## [105,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
## [106,]  -0.005687723000   0.229378922       0.0000       0.0000 0.0012
## [107,]  -0.004266201771   0.265671044       0.0000       0.0000 0.0012
## [108,]   0.010980529400   0.537342302       0.0000       0.0000 0.0028
## [109,]   0.009179044971   0.332004288       0.0000       0.0000 0.0012
## [110,]   0.004941068362   0.567887270       0.0000       0.0000 0.0028
## [111,]  -0.010249281112   0.364510848       0.0000       0.0000 0.0008
## [112,]  -0.002035893479   0.101794674       0.0000       0.0000 0.0004
## [113,]   0.043430110262   1.047290891       0.0000       0.0000 0.0024
## [114,]   0.020150766173   0.702785330       0.0000       0.0000 0.0016
## [115,]  -0.005911480500   0.258599896       0.0000       0.0000 0.0008
## [116,]   0.011967896273   0.421889994       0.0000       0.0000 0.0016
## [117,]  -0.000729699172   0.027664490       0.0000       0.0000 0.0008
## [118,]  -0.000992232993   0.049611650       0.0000       0.0000 0.0004
## [119,]  -0.001323019899   0.147002855       0.0000       0.0000 0.0008
## [120,]  -0.002522412246   0.126120612       0.0000       0.0000 0.0004
## [121,]   0.000325557666   0.016277883       0.0000       0.0000 0.0004
## [122,]  -0.000021164223   0.455791942       0.0000       0.0000 0.0016
## [123,]   0.007324788720   0.508966833       0.0000       0.0000 0.0012
## [124,]  -0.003358913378   0.178792074       0.0000       0.0000 0.0012
## [125,]   0.035226104321   1.074201245       0.0000       0.0000 0.0020
## [126,]   0.044477099903   0.993260768       0.0000       0.0000 0.0028
## [127,]   0.005333940447   0.477093079       0.0000       0.0000 0.0016
## [128,]   0.002288761537   0.554182301       0.0000       0.0000 0.0020
## [129,]  -0.008400038421   0.395490032       0.0000       0.0000 0.0008
## [130,]  -0.000009450959   0.069842095       0.0000       0.0000 0.0008
## [131,]  -0.001983314158   0.099165708       0.0000       0.0000 0.0004
## [132,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
## [133,]   0.000114338528   0.005716926       0.0000       0.0000 0.0004
## [134,]   0.016709985307   0.549877329       0.0000       0.0000 0.0016
## [135,]  -0.006002317416   0.258929275       0.0000       0.0000 0.0008
## [136,]  -0.031407483462   1.019996000       0.0000       0.0000 0.0020
## [137,]   0.012535734443   0.484714264       0.0000       0.0000 0.0012
## [138,]   0.000101355067   0.438174348       0.0000       0.0000 0.0012
## [139,]  -0.004281830577   0.267514223       0.0000       0.0000 0.0012
## [140,]  -0.000223446439   0.011172322       0.0000       0.0000 0.0004
## [141,]   0.002691485554   0.533404001       0.0000       0.0000 0.0016
## [142,]  -0.000176858920   0.355191337       0.0000       0.0000 0.0008
## [143,]   0.008769933611   0.406370745       0.0000       0.0000 0.0008
## [144,]  -0.005866888211   0.248711272       0.0000       0.0000 0.0008
## [145,]   0.015877822570   0.596828480       0.0000       0.0000 0.0020
## [146,]   0.021387841396   0.638318370       0.0000       0.0000 0.0020
## [147,]   0.009586465649   0.783295324       0.0000       0.0000 0.0016
## [148,]   0.006972286804   0.351091807       0.0000       0.0000 0.0016
## [149,]  -0.007560189344   0.670910300       0.0000       0.0000 0.0020
## [150,]   0.047882384973   1.580559900       0.0000       0.0000 0.0020
## [151,]   0.049368500749   1.418835177       0.0000       0.0000 0.0016
## [152,]   0.273313855086   4.460688733       0.0000       0.0000 0.0052
## [153,]  -0.003636326310   0.195720095       0.0000       0.0000 0.0016
## [154,]   0.043095524283   0.978527565       0.0000       0.0000 0.0040
## [155,]  -0.006351782682   0.371913426       0.0000       0.0000 0.0016
## [156,]   0.000716500691   0.100669890       0.0000       0.0000 0.0008
## [157,]   0.003783065271   0.175467622       0.0000       0.0000 0.0008
## [158,]   0.005871385873   0.405099726       0.0000       0.0000 0.0008
## [159,]  -0.005706081471   0.655529544       0.0000       0.0000 0.0016
## [160,]  -0.008286059962   0.308772109       0.0000       0.0000 0.0016
## [161,]  -0.012291229624   0.323429589       0.0000       0.0000 0.0024
## [162,]   0.001493263593   0.234540743       0.0000       0.0000 0.0024
## [163,]  -0.001983314158   0.099165708       0.0000       0.0000 0.0004
## [164,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
## [165,]   0.003102652583   0.139844148       0.0000       0.0000 0.0008
## [166,]  -0.008423754939   0.287213847       0.0000       0.0000 0.0012
## [167,]  -0.003983753377   0.146258551       0.0000       0.0000 0.0016
## [168,]  -0.010178789835   0.321780791       0.0000       0.0000 0.0012
## [169,]   0.016687047354   0.707970358       0.0000       0.0000 0.0008
## [170,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
## [171,]   0.024376439630   0.817705870       0.0000       0.0000 0.0012
## [172,]   0.003705221818   0.226259975       0.0000       0.0000 0.0012
## [173,]   0.008908675837   0.434659818       0.0000       0.0000 0.0016
## [174,]  -0.000674292767   0.118839701       0.0000       0.0000 0.0008
## [175,]   0.001377480593   0.143169895       0.0000       0.0000 0.0012
## [176,]   0.002363591166   0.118179558       0.0000       0.0000 0.0004
## [177,]   0.006265900792   0.367832183       0.0000       0.0000 0.0008
## [178,]  -0.000410276679   0.246912386       0.0000       0.0000 0.0012
## [179,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
## [180,]   0.000114338528   0.005716926       0.0000       0.0000 0.0004
## [181,]  -0.001157612892   0.204595127       0.0000       0.0000 0.0020
## [182,]  -0.002078263629   0.073476308       0.0000       0.0000 0.0008
## [183,]  -0.008988077028   0.602326651       0.0000       0.0000 0.0024
## [184,]   0.000514896289   0.025744814       0.0000       0.0000 0.0004
## [185,]  -0.001299671182   0.260156582       0.0000       0.0000 0.0016
## [186,]   0.000480950928   0.024047546       0.0000       0.0000 0.0004
## [187,]  -0.005440443915   0.436579895       0.0000       0.0000 0.0012
## [188,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
## [189,]  -0.005798703173   0.194504582       0.0000       0.0000 0.0012
## [190,]   0.001749630365   0.087481518       0.0000       0.0000 0.0004
## [191,]   0.032770682495   0.959331107       0.0000       0.0000 0.0020
## [192,]   0.008839284821   0.365588177       0.0000       0.0000 0.0008
## [193,]  -0.028860237200   0.891009296       0.0000       0.0000 0.0016
## [194,]  -0.015918178493   0.808026318       0.0000       0.0000 0.0028
## [195,]  -0.016050503226   0.472468086       0.0000       0.0000 0.0016
## [196,]  -0.000573347847   0.119732807       0.0000       0.0000 0.0012
## [197,]   0.030984896052   1.042390234       0.0000       0.0000 0.0024
## [198,]   0.019040237252   0.804240413       0.0000       0.0000 0.0024
## [199,]  -0.018892547228   0.718803584       0.0000       0.0000 0.0020
## [200,]   0.006591254178   0.685307845       0.0000       0.0000 0.0008
## [201,]   0.035863985187   1.047390418       0.0000       0.0000 0.0020
## [202,]  -0.021585130450   1.181459299       0.0000       0.0000 0.0024
## [203,]  -0.012447587862   0.927931714       0.0000       0.0000 0.0024
## [204,]  -0.011818187563   0.361144266       0.0000       0.0000 0.0024
## [205,]   0.005330297486   0.242479956       0.0000       0.0000 0.0008
## [206,]  -0.000506252733   0.025312637       0.0000       0.0000 0.0004
## [207,]  -0.106976116780   4.094897938       0.0000       0.0000 0.0020
## [208,]   0.002668809167   0.133440458       0.0000       0.0000 0.0004
## [209,]  -0.022690691209   0.629259335       0.0000       0.0000 0.0024
## [210,]   0.004923672990   0.610278562       0.0000       0.0000 0.0016
## [211,]   0.010279888662   0.435894596       0.0000       0.0000 0.0008
## [212,]   0.000377287939   0.265748516       0.0000       0.0000 0.0016
## [213,]  -0.012196093930   0.434055714       0.0000       0.0000 0.0020
## [214,]   0.014325004919   0.693749283       0.0000       0.0000 0.0016
## [215,]   0.000534531027   0.253645130       0.0000       0.0000 0.0008
## [216,]  -0.000694836766   0.053495280       0.0000       0.0000 0.0008
## [217,]   0.000113095261   0.128126558       0.0000       0.0000 0.0012
## [218,]  -0.054430628780   1.600389856       0.0000       0.0000 0.0016
## [219,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
## [220,]   0.006333168562   1.398435348       0.0000       0.0000 0.0008
## [221,]   0.146476631875   5.566990874       0.0000       0.0000 0.0020
## [222,]  -0.012505470337   1.602043820       0.0000       0.0000 0.0036
## [223,]  -0.027055302348   1.304193436       0.0000       0.0000 0.0008
## [224,] -43.610711820194  90.664619761    -283.6853       0.0000 0.2036
## [225,] 114.941153991638 163.716603745       0.0000     419.3540 0.3412
## [226,] 216.623293997141 154.532791453       0.0000     425.6378 0.6940
## [227,]   0.038534102688   0.914462329       0.0000       0.0000 0.0024
## [228,]  -0.431685193282   6.623088154       0.0000       0.0000 0.0068
## [229,]   0.030749100014   1.316689998       0.0000       0.0000 0.0020
## [230,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
## [231,]  -0.007965831545   0.414842136       0.0000       0.0000 0.0008
## [232,]   0.003009641447   0.206171671       0.0000       0.0000 0.0008
## [233,]  -0.024384424829   0.910756994       0.0000       0.0000 0.0008
## [234,]   0.074662233755   1.523125789       0.0000       0.0000 0.0036
## [235,]  -0.001418739586   0.127764794       0.0000       0.0000 0.0012
## [236,]  -0.002862113274   0.319645591       0.0000       0.0000 0.0012
## [237,]   0.002870554898   0.103876232       0.0000       0.0000 0.0008
## [238,]  -0.003443891433   0.172194572       0.0000       0.0000 0.0004
## [239,]  -0.011537605644   0.733820149       0.0000       0.0000 0.0032
## [240,]   0.124497999723   5.504027503       0.0000       0.0000 0.0016
## [241,]  -0.024041540868   1.193313391       0.0000       0.0000 0.0028
## [242,]   0.096860796697   2.702148443       0.0000       0.0000 0.0032
## [243,]  -0.004821969126   0.182686654       0.0000       0.0000 0.0012
## [244,]  -0.243625039744   6.582629395       0.0000       0.0000 0.0024
## [245,]  -0.007606490432   0.281577056       0.0000       0.0000 0.0012
## [246,]  -0.016893193508   2.346384818       0.0000       0.0000 0.0012
## [247,]  -0.000839766869   0.244724112       0.0000       0.0000 0.0012
## [248,]  -0.009234842745   0.809042205       0.0000       0.0000 0.0036
## [249,]   0.071549932110   1.820621158       0.0000       0.0000 0.0036
## [250,]  -0.006208641706   0.486792125       0.0000       0.0000 0.0016
## [251,]   0.003082670358   0.577047742       0.0000       0.0000 0.0024
## [252,]  -0.024452592396   0.897680321       0.0000       0.0000 0.0028
## [253,]   0.000982782034   0.049139102       0.0000       0.0000 0.0004
## [254,]  -0.000223446439   0.011172322       0.0000       0.0000 0.0004
## [255,]  -0.005323119457   0.255223829       0.0000       0.0000 0.0008
## [256,]   0.011363917537   0.577134624       0.0000       0.0000 0.0032
## [257,]   0.004932951905   0.246647595       0.0000       0.0000 0.0004
## [258,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
## [259,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
## [260,]  -0.003443891433   0.172194572       0.0000       0.0000 0.0004
## [261,]  -0.004013380452   0.200669023       0.0000       0.0000 0.0004
## [262,]  -0.004524812838   0.268533078       0.0000       0.0000 0.0016
## [263,]  -0.008278458855   0.347261337       0.0000       0.0000 0.0008
## [264,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
## [265,]  -0.073211209144   2.615423506       0.0000       0.0000 0.0020
## [266,]  -0.021385907113   0.836327645       0.0000       0.0000 0.0016
## [267,]  -0.122862711508   4.466487848       0.0000       0.0000 0.0016
## [268,]  -0.027256861660   1.238201870       0.0000       0.0000 0.0008
## [269,]   0.011361884524   0.568094226       0.0000       0.0000 0.0004
## [270,]   0.004098426998   0.177440214       0.0000       0.0000 0.0008
## [271,]  -0.036676055872   1.670438226       0.0000       0.0000 0.0008
## [272,]   0.004663223388   0.260466621       0.0000       0.0000 0.0012
## [273,]   0.001963729548   0.251380777       0.0000       0.0000 0.0012
## [274,]  -0.023914001366   0.927831912       0.0000       0.0000 0.0028
## [275,]   0.010555931994   0.525316272       0.0000       0.0000 0.0012
## [276,]   0.019584670333   0.901433513       0.0000       0.0000 0.0012
## [277,]  -0.000223446439   0.011172322       0.0000       0.0000 0.0004
## [278,]  -0.028000666868   1.191604755       0.0000       0.0000 0.0020
## [279,]   0.017998846198   1.119293243       0.0000       0.0000 0.0028
## [280,]  -0.009487179784   0.334951515       0.0000       0.0000 0.0016
## [281,]   0.001445214785   0.142299300       0.0000       0.0000 0.0012
## [282,]  -0.132384455164   2.937537176       0.0000       0.0000 0.0028
## [283,]   0.021700515151   0.789434448       0.0000       0.0000 0.0012
## [284,]  -0.011210143508   0.451510686       0.0000       0.0000 0.0016
## [285,]  -0.005697884150   0.224570362       0.0000       0.0000 0.0024
## [286,]   0.140477498358   3.417955205       0.0000       0.0000 0.0028
## [287,]   0.000982782034   0.049139102       0.0000       0.0000 0.0004
## [288,]  -0.012140579131   0.771038532       0.0000       0.0000 0.0020
## [289,]   0.019404727130   1.142571797       0.0000       0.0000 0.0024
## [290,]  -0.002632041291   0.131602065       0.0000       0.0000 0.0004
## [291,]  -0.032040738551   1.348885426       0.0000       0.0000 0.0032
## [292,]   0.004932951905   0.246647595       0.0000       0.0000 0.0004
## [293,]  -0.001895739489   0.181896099       0.0000       0.0000 0.0012
## [294,]   0.002824298710   0.198846841       0.0000       0.0000 0.0008
## [295,]  -0.002035893479   0.101794674       0.0000       0.0000 0.0004
## [296,]  -0.002240990713   0.300659505       0.0000       0.0000 0.0016
## [297,]   0.008356667298   0.505926875       0.0000       0.0000 0.0012
## [298,]  -0.007673193710   0.911612147       0.0000       0.0000 0.0020
## [299,]   0.027217828715   0.715671423       0.0000       0.0000 0.0028
## [300,]  -0.032116270313   1.165611455       0.0000       0.0000 0.0016
## [301,]   0.009045673591   0.452283680       0.0000       0.0000 0.0004
## [302,]   0.002635010910   0.416662053       0.0000       0.0000 0.0024
## [303,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
## [304,]   0.001735869291   0.086793465       0.0000       0.0000 0.0004
## [305,]   0.006008546638   0.658115498       0.0000       0.0000 0.0016
## [306,]   0.000372948594   0.570793624       0.0000       0.0000 0.0016
## [307,]  -0.007137469416   0.279235206       0.0000       0.0000 0.0008
## [308,]   0.003874056876   0.252286809       0.0000       0.0000 0.0008
## [309,]   0.330215183117   7.534931305       0.0000       0.0000 0.0036
## [310,]  -0.022306792333   1.509933913       0.0000       0.0000 0.0028
## [311,]   0.020213747679   0.554660864       0.0000       0.0000 0.0016
## [312,]   0.001789972319   0.069719921       0.0000       0.0000 0.0008
## [313,]  -0.048491637159   1.696511066       0.0000       0.0000 0.0020
## [314,]   0.021856361188   0.723960268       0.0000       0.0000 0.0016
## [315,]   0.010418325083   1.393885583       0.0000       0.0000 0.0020
## [316,]  -0.000992232993   0.049611650       0.0000       0.0000 0.0004
## [317,]  -0.006941944990   0.288695619       0.0000       0.0000 0.0012
## [318,]   0.121389897186   2.890339926       0.0000       0.0000 0.0048
## [319,]   0.051092838515   1.321430001       0.0000       0.0000 0.0020
## [320,]   0.011422860622   0.481460084       0.0000       0.0000 0.0012
## [321,]  -0.039969613867   1.316548298       0.0000       0.0000 0.0012
## [322,]  -0.010503303935   0.351600584       0.0000       0.0000 0.0020
## [323,]  -0.005235203740   0.263956895       0.0000       0.0000 0.0012
## [324,]  -0.029719106666   1.485955333       0.0000       0.0000 0.0004
## [325,]  -0.039411945912   1.657208745       0.0000       0.0000 0.0024
## [326,]   0.012617798440   0.607210866       0.0000       0.0000 0.0008
## [327,]  -0.014750435159   0.774328638       0.0000       0.0000 0.0020
## [328,]  -0.001017197620   0.154424440       0.0000       0.0000 0.0008
## [329,]   0.003325359251   0.379808506       0.0000       0.0000 0.0008
## [330,]   0.000594073129   0.582179826       0.0000       0.0000 0.0020
## [331,]  -0.002160016848   0.487914391       0.0000       0.0000 0.0008
## [332,]   0.026456049282   1.376786782       0.0000       0.0000 0.0008
## [333,]  -0.025829962128   1.263421100       0.0000       0.0000 0.0012
## [334,]   0.005790570615   0.503450964       0.0000       0.0000 0.0012
## [335,]   0.017987670344   0.899383517       0.0000       0.0000 0.0004
## [336,]  -0.025702672241   0.964858375       0.0000       0.0000 0.0016
## [337,]   0.035819971656   1.182461390       0.0000       0.0000 0.0020
## [338,]  -0.035750916480   1.374938602       0.0000       0.0000 0.0020
## [339,]   0.025120968138   0.981803018       0.0000       0.0000 0.0020
## [340,]   0.026933278504   1.045675694       0.0000       0.0000 0.0024
## [341,]   0.044441715123   1.723055635       0.0000       0.0000 0.0016
## [342,]   0.001141533589   0.551766679       0.0000       0.0000 0.0020
## [343,]   0.003357313260   0.206259510       0.0000       0.0000 0.0012
## [344,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
## [345,]   0.046685249680   1.545990008       0.0000       0.0000 0.0016
## [346,]   0.013301234958   1.089304253       0.0000       0.0000 0.0024
## [347,]  -0.020768062830   1.248114295       0.0000       0.0000 0.0008
## [348,]  -0.061832547676   2.240567797       0.0000       0.0000 0.0016
## [349,]   0.009045673591   0.452283680       0.0000       0.0000 0.0004
## [350,]  -0.052156069430   1.143059595       0.0000       0.0000 0.0040
## [351,]   0.003283538170   0.150587569       0.0000       0.0000 0.0008
## [352,]  -0.042440734926   1.174658904       0.0000       0.0000 0.0024
## [353,]  -0.005738808129   0.196816029       0.0000       0.0000 0.0020
## [354,]  -0.004605030467   0.339134877       0.0000       0.0000 0.0020
## [355,]  -0.020372090130   0.628385837       0.0000       0.0000 0.0024
## [356,]  -0.005903625313   0.553188019       0.0000       0.0000 0.0024
## [357,]   0.000941464799   0.430028453       0.0000       0.0000 0.0016
## [358,]   0.088836660819   2.875998425       0.0000       0.0000 0.0040
## [359,]  -0.003772726668   0.701723695       0.0000       0.0000 0.0008
## [360,]  -0.018170955609   0.721422564       0.0000       0.0000 0.0012
## [361,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
## [362,]   0.016912885060   1.005971241       0.0000       0.0000 0.0020
## [363,]  -0.007615822093   0.766351847       0.0000       0.0000 0.0024
## [364,]   0.075385031377   2.348979139       0.0000       0.0000 0.0028
## [365,]   0.005408439970   0.376193374       0.0000       0.0000 0.0008
## [366,]   0.011317926551   0.551871961       0.0000       0.0000 0.0012
## [367,]  -0.004292502876   0.312724305       0.0000       0.0000 0.0012
## [368,]   0.018978150320   0.687139654       0.0000       0.0000 0.0012
## [369,]   0.029297966152   0.821103300       0.0000       0.0000 0.0028
## [370,]   0.025550648104   1.438322175       0.0000       0.0000 0.0016
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## [372,]   0.004000855426   0.373404084       0.0000       0.0000 0.0012
## [373,]  -0.004871434138   0.205321311       0.0000       0.0000 0.0020
## [374,]   0.053894914123   1.339782259       0.0000       0.0000 0.0032
## [375,]  -0.039697689244   1.082627946       0.0000       0.0000 0.0020
## [376,]  -0.008001465826   0.425330504       0.0000       0.0000 0.0016
## [377,]   0.006520702235   0.326035112       0.0000       0.0000 0.0004
## [378,]   0.020427598144   0.993687213       0.0000       0.0000 0.0016
## [379,]   0.015676372845   0.550062823       0.0000       0.0000 0.0020
## [380,]  -0.003657764112   0.159731550       0.0000       0.0000 0.0016
## [381,]  -0.011104123059   0.366766749       0.0000       0.0000 0.0012
## [382,]   0.186790333798   6.451118923       0.0000       0.0000 0.0032
## [383,]   0.064820612629   2.467264063       0.0000       0.0000 0.0020
## [384,]  -0.001469016866   0.073450843       0.0000       0.0000 0.0004
## [385,]  -0.020061758084   1.166110146       0.0000       0.0000 0.0024
## [386,]   0.010772193710   0.564277196       0.0000       0.0000 0.0032
## [387,]   0.002998330781   0.149916539       0.0000       0.0000 0.0004
## [388,]   0.012511535606   0.837464098       0.0000       0.0000 0.0012
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## [401,]   0.087639814106   3.614058124       0.0000       0.0000 0.0028
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## [406,]  -0.000004176959   0.173045028       0.0000       0.0000 0.0012
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## [410,]   0.104113163095   3.242627644       0.0000       0.0000 0.0028
## [411,]   0.031469640149   1.824931709       0.0000       0.0000 0.0012
## [412,]   0.089294301104   2.101418263       0.0000       0.0000 0.0036
## [413,]  -0.112772145551   3.612682875       0.0000       0.0000 0.0028
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## [416,]   0.009031574261   0.445896149       0.0000       0.0000 0.0008
## [417,]  -0.053753270313   1.526042712       0.0000       0.0000 0.0032
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## [419,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
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## [428,]   0.044493617606   2.429070646       0.0000       0.0000 0.0012
## [429,]  -0.011041382894   0.494276156       0.0000       0.0000 0.0020
## [430,]  -0.005300739115   1.100631852       0.0000       0.0000 0.0024
## [431,]   0.004422857492   0.445818249       0.0000       0.0000 0.0016
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## [433,]   0.032315788170   1.258143600       0.0000       0.0000 0.0024
## [434,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
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## [442,]   0.003221524900   0.358913270       0.0000       0.0000 0.0012
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## [445,]  -0.028606198853   1.153449294       0.0000       0.0000 0.0012
## [446,]  -0.002822170884   0.201170530       0.0000       0.0000 0.0016
## [447,]  -0.033901322702   1.316591568       0.0000       0.0000 0.0012
## [448,]   0.007110222365   0.265085326       0.0000       0.0000 0.0008
## [449,]   0.031297141102   1.510225029       0.0000       0.0000 0.0028
## [450,]  -0.076224146477   1.937546730       0.0000       0.0000 0.0036
## [451,]  -0.017480282958   0.466338960       0.0000       0.0000 0.0028
## [452,]   0.016525789324   0.950602952       0.0000       0.0000 0.0024
## [453,]   0.026877621762   1.282833466       0.0000       0.0000 0.0024
## [454,]   0.002965021087   0.480228996       0.0000       0.0000 0.0016
## [455,]   0.003394399523   0.169719976       0.0000       0.0000 0.0004
## [456,]  -0.003044439250   1.592086850       0.0000       0.0000 0.0024
## [457,]  -0.150731615437   3.470374080       0.0000       0.0000 0.0032
## [458,]  -0.007909118432   0.695773771       0.0000       0.0000 0.0016
## [459,]   0.244384427227   4.508046174       0.0000       0.0000 0.0044
## [460,]  -0.078068593117   2.942938625       0.0000       0.0000 0.0016
## [461,]   0.001993604705   0.437600640       0.0000       0.0000 0.0008
## [462,]  -0.046987331722   2.020178663       0.0000       0.0000 0.0020
## [463,]   0.014241901875   0.723358170       0.0000       0.0000 0.0008
## [464,]  -0.022336593181   0.635456827       0.0000       0.0000 0.0016
## [465,]  -0.000521349754   0.225396467       0.0000       0.0000 0.0012
## [466,]  -0.008542714468   0.257753807       0.0000       0.0000 0.0012
## [467,]  -0.026720539165   0.865427173       0.0000       0.0000 0.0024
## [468,]  -0.007688881201   0.273260984       0.0000       0.0000 0.0008
## [469,]  -0.021129567278   0.753094440       0.0000       0.0000 0.0016
## [470,]   0.003552358202   1.300608268       0.0000       0.0000 0.0020
## [471,]  -0.080362431264   2.105643388       0.0000       0.0000 0.0024
## [472,]   0.040064755881   1.230047602       0.0000       0.0000 0.0016
## [473,]  -0.129070271227   3.464173182       0.0000       0.0000 0.0040
## [474,]  -0.297532957739   6.945318586       0.0000       0.0000 0.0040
## [475,]   0.017023584789   0.603708555       0.0000       0.0000 0.0020
## [476,]  -0.003355896400   0.167794820       0.0000       0.0000 0.0004
## [477,]   0.001878440183   0.093922009       0.0000       0.0000 0.0004
## [478,]   0.006539447203   0.345393856       0.0000       0.0000 0.0016
## [479,]  -0.002813324968   0.331923970       0.0000       0.0000 0.0012
## [480,]  -0.003887658935   0.419035372       0.0000       0.0000 0.0012
## [481,]  -0.016335095302   0.816754765       0.0000       0.0000 0.0004
## [482,]   0.110136253185   2.633185070       0.0000       0.0000 0.0032
## [483,]  -0.039065457713   1.805020878       0.0000       0.0000 0.0016
## [484,]   0.011517481521   0.510397379       0.0000       0.0000 0.0020
## [485,]  -0.003520569152   0.279380787       0.0000       0.0000 0.0016
## [486,]   0.006265900792   0.367832183       0.0000       0.0000 0.0008
## [487,]   0.008296660881   0.294063054       0.0000       0.0000 0.0008
## [488,]  -0.001997654801   0.590515320       0.0000       0.0000 0.0016
## [489,]   0.013899617416   0.669370810       0.0000       0.0000 0.0020
## [490,]   0.001939435752   0.159010905       0.0000       0.0000 0.0008
## [491,]   0.005692162025   0.188201053       0.0000       0.0000 0.0012
## [492,]  -0.005285543407   0.330738920       0.0000       0.0000 0.0012
## [493,]   0.061725447421   2.424814491       0.0000       0.0000 0.0012
## [494,]   0.030222079821   1.249347692       0.0000       0.0000 0.0012
## [495,]   0.018057633094   2.116524995       0.0000       0.0000 0.0028
## [496,]  -0.007129916935   0.287903012       0.0000       0.0000 0.0012
## [497,]  -0.541555998660  11.620297129       0.0000       0.0000 0.0036
## [498,]  -0.006390754414   0.229388579       0.0000       0.0000 0.0008
## [499,]   0.031312142116   1.281608472       0.0000       0.0000 0.0016
## [500,]  -0.006093930366   0.267615872       0.0000       0.0000 0.0008
## [501,]  -0.003763328334   0.264187657       0.0000       0.0000 0.0012
## [502,]   0.004737180240   0.247394982       0.0000       0.0000 0.0012
## [503,]  -0.016505048345   0.440994222       0.0000       0.0000 0.0016
## [504,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
## [505,]   0.007845541749   0.277382709       0.0000       0.0000 0.0008
## [506,]   0.001162382295   0.703965250       0.0000       0.0000 0.0020
## [507,]  -0.000790719781   0.051808534       0.0000       0.0000 0.0012
## [508,]  -0.091292278515   4.275619929       0.0000       0.0000 0.0012
## [509,]   0.019919709703   0.587879829       0.0000       0.0000 0.0016
## [510,]  -0.028377395534   1.281611552       0.0000       0.0000 0.0012
## [511,]   0.000156778237   0.315960239       0.0000       0.0000 0.0012
## [512,]  -0.011882560201   0.424224410       0.0000       0.0000 0.0008
## [513,]  -0.002583074826   0.294520678       0.0000       0.0000 0.0016
## [514,]   0.001735869291   0.086793465       0.0000       0.0000 0.0004
## [515,]  -0.013190897425   0.396876298       0.0000       0.0000 0.0012
## [516,]   0.176560603886   6.199212782       0.0000       0.0000 0.0016
## [517,]   0.039286278573   1.556759180       0.0000       0.0000 0.0016
## [518,]   0.001344180444   0.261527347       0.0000       0.0000 0.0016
## [519,]   0.011154120929   0.857738114       0.0000       0.0000 0.0024
## [520,]  -0.427929774266  11.078044851       0.0000       0.0000 0.0028
## [521,]  -0.026306605605   1.161547758       0.0000       0.0000 0.0020
## [522,]   0.010993171075   0.479989933       0.0000       0.0000 0.0016
## [523,]   0.017421997496   0.740392942       0.0000       0.0000 0.0024
## [524,]  -0.007006927076   0.214857725       0.0000       0.0000 0.0016
## [525,]  -0.003311622298   0.407295643       0.0000       0.0000 0.0012
## [526,]  -0.017863702868   0.893185143       0.0000       0.0000 0.0004
## [527,]   0.004599772424   0.241424062       0.0000       0.0000 0.0008
## [528,]   0.002441129469   0.076734570       0.0000       0.0000 0.0012
## [529,]  -0.017193796479   0.893826370       0.0000       0.0000 0.0008
## [530,]  -0.001069488608   0.053474430       0.0000       0.0000 0.0004
## [531,]  -0.002542146212   0.104884808       0.0000       0.0000 0.0008
## [532,]  -0.005109810825   0.255490541       0.0000       0.0000 0.0004
## [533,]  -0.066742999041   1.868340877       0.0000       0.0000 0.0020
## [534,]  -0.010184112403   0.348100098       0.0000       0.0000 0.0024
## [535,]   0.001013628373   0.249770816       0.0000       0.0000 0.0008
## [536,]   0.004624961009   0.180505448       0.0000       0.0000 0.0008
## [537,]  -0.003443891433   0.172194572       0.0000       0.0000 0.0004
## [538,]   0.005069514481   0.226840132       0.0000       0.0000 0.0012
## [539,]   0.008768391619   0.482933392       0.0000       0.0000 0.0012
## [540,]   0.024825452404   0.985752854       0.0000       0.0000 0.0016
## [541,]  -0.005646813793   0.215296180       0.0000       0.0000 0.0012
## [542,]  -0.086282077491   3.125296211       0.0000       0.0000 0.0024
## [543,]  -0.003342384400   1.433772545       0.0000       0.0000 0.0024
## [544,]   0.009527491364   0.522016055       0.0000       0.0000 0.0016
## [545,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
## [546,]  -0.015643548175   0.401912056       0.0000       0.0000 0.0016
## [547,]   0.017902235826   0.895111791       0.0000       0.0000 0.0004
## [548,]  -0.054257903154   1.919163579       0.0000       0.0000 0.0008
## [549,]   0.018349443137   0.954060522       0.0000       0.0000 0.0024
## [550,]  -0.111948917840   3.366369321       0.0000       0.0000 0.0012
## [551,]   0.089835683473   1.959253375       0.0000       0.0000 0.0044
## [552,]  -0.032817598706   1.265497481       0.0000       0.0000 0.0016
## [553,]  -0.007185294658   0.359264733       0.0000       0.0000 0.0004
## [554,]  -0.019247395934   1.139166233       0.0000       0.0000 0.0016
## [555,]  -0.021713356252   0.873775256       0.0000       0.0000 0.0016
## [556,]   0.008364806925   0.481739860       0.0000       0.0000 0.0012
## [557,]   0.000753009410   0.367200383       0.0000       0.0000 0.0012
## [558,]  -0.040549500886   1.348765216       0.0000       0.0000 0.0016
## [559,]   0.013701614550   0.737832073       0.0000       0.0000 0.0008
## [560,]  -0.015928549155   0.603835731       0.0000       0.0000 0.0016
## [561,]  -0.001828942650   0.259421800       0.0000       0.0000 0.0012
## [562,]  -0.071508039564   2.749708122       0.0000       0.0000 0.0012
## [563,]   0.001381744906   0.278854506       0.0000       0.0000 0.0020
## [564,]  -0.043497089570   1.418740784       0.0000       0.0000 0.0024
## [565,]  -0.188329757428   4.130627661       0.0000       0.0000 0.0028
## [566,]  -0.079912936803   4.310741042       0.0000       0.0000 0.0020
## [567,]  -0.026527163782   1.051055190       0.0000       0.0000 0.0012
## [568,]  -0.002627411280   0.662451285       0.0000       0.0000 0.0020
## [569,]  -0.002234051698   0.308409083       0.0000       0.0000 0.0012
## [570,]   0.000507078624   0.025353931       0.0000       0.0000 0.0004
## [571,]  -0.211485483590   4.659073861       0.0000       0.0000 0.0032
## [572,]   0.017215252917   0.789823708       0.0000       0.0000 0.0024
## [573,]  -0.145928457079   3.946618040       0.0000       0.0000 0.0020
## [574,]   0.005129326795   0.432702329       0.0000       0.0000 0.0012
## [575,]  -0.025034838295   1.020516622       0.0000       0.0000 0.0012
## [576,]   0.000000000000   0.000000000       0.0000       0.0000 0.0000
## [577,]  -0.059857362648   2.821409134       0.0000       0.0000 0.0024
## [578,]  -0.082423741515   2.711199122       0.0000       0.0000 0.0024
## [579,]  -0.001539630212   0.135373632       0.0000       0.0000 0.0008
## [580,]  -0.001881249357   0.102091001       0.0000       0.0000 0.0008
## [581,]  -0.273424567937   4.702648379       0.0000       0.0000 0.0044
## [582,]  -0.014882700089   1.074945145       0.0000       0.0000 0.0020
## [583,]  -0.051432024167   1.498641348       0.0000       0.0000 0.0024
## [584,]  -0.030154159928   1.313038874       0.0000       0.0000 0.0020
## [585,]  -0.015113578472   0.927404907       0.0000       0.0000 0.0028
## [586,]   0.013488312390   0.529563578       0.0000       0.0000 0.0012
## [587,]  -0.066288396181   1.942594865       0.0000       0.0000 0.0028
## [588,]   0.005366907139   0.509481097       0.0000       0.0000 0.0024
## [589,]  -0.075516110774   3.081729763       0.0000       0.0000 0.0020
## [590,]  -0.006622353921   0.305550680       0.0000       0.0000 0.0012
## [591,]   0.030377516261   1.381042758       0.0000       0.0000 0.0012
## [592,]  -0.027925282276   1.703327605       0.0000       0.0000 0.0016
## [593,]  -0.006673696594   0.796966429       0.0000       0.0000 0.0016
## [594,]  -0.003944013945   0.404333389       0.0000       0.0000 0.0008
## [595,]   0.041033325033   1.410800229       0.0000       0.0000 0.0028
## [596,]  -0.088249846552   2.585429286       0.0000       0.0000 0.0028
## [597,]   0.076040591351   2.087619634       0.0000       0.0000 0.0016
## [598,]  -0.005347921639   0.299900920       0.0000       0.0000 0.0016
## [599,]  -0.003443891433   0.172194572       0.0000       0.0000 0.0004
## [600,]  -0.089966071692   2.943008324       0.0000       0.0000 0.0024
## [601,]  -0.007537898449   0.509725000       0.0000       0.0000 0.0020
## [602,]   0.000355426098   0.102414359       0.0000       0.0000 0.0008
## [603,]   0.023383775505   0.768320558       0.0000       0.0000 0.0016
## [604,]  -0.010267419005   0.582536774       0.0000       0.0000 0.0008
## [605,]   0.012836131413   0.476034309       0.0000       0.0000 0.0012
## [606,]  -0.027646032585   0.885966621       0.0000       0.0000 0.0016
## [607,]  -0.022748118392   1.029150878       0.0000       0.0000 0.0012
## [608,]  -0.021068459704   1.133299454       0.0000       0.0000 0.0016
## [609,]  -0.006110262875   0.191139753       0.0000       0.0000 0.0012
## [610,]  -0.014722035733   1.005118281       0.0000       0.0000 0.0036
## [611,]   0.025729418296   0.814658457       0.0000       0.0000 0.0012
## [612,]   0.015125634248   0.955354419       0.0000       0.0000 0.0028
## [613,]  -0.005630800949   0.380966473       0.0000       0.0000 0.0012
## [614,]   0.005567069839   0.813550005       0.0000       0.0000 0.0020
## [615,]  -0.005487556507   0.200195669       0.0000       0.0000 0.0008
## [616,]  -0.000506252733   0.025312637       0.0000       0.0000 0.0004
## [617,]  -0.003764185227   0.371384972       0.0000       0.0000 0.0028
## [618,]   0.012134801995   0.606740100       0.0000       0.0000 0.0004
## [619,]  -0.001384675744   0.178573365       0.0000       0.0000 0.0008
## [620,]   0.202873356065   4.580754569       0.0000       0.0000 0.0036
## [621,]  -0.001983314158   0.099165708       0.0000       0.0000 0.0004
## [622,]   0.007013546677   0.255566204       0.0000       0.0000 0.0008
## [623,]  -0.036270976639   1.822863150       0.0000       0.0000 0.0024
## [624,]   0.000848293967   0.183837266       0.0000       0.0000 0.0016
## [625,]  -0.011977627499   0.425577713       0.0000       0.0000 0.0008
## [626,]  -0.003217057662   0.332184789       0.0000       0.0000 0.0024
## [627,]   0.001749630365   0.087481518       0.0000       0.0000 0.0004
## [628,]  -0.026009904267   0.796874583       0.0000       0.0000 0.0028
## [629,]  -0.046105393163   1.461744462       0.0000       0.0000 0.0016
## [630,]  -0.006275205220   0.604332575       0.0000       0.0000 0.0020
## [631,]  -0.002603875800   0.302679952       0.0000       0.0000 0.0016
## [632,]   0.052034449028   2.375218521       0.0000       0.0000 0.0012
## [633,]  -0.026511033843   1.144500222       0.0000       0.0000 0.0012
## [634,]  -0.005099673018   0.254983651       0.0000       0.0000 0.0004
## [635,]  -0.014182404061   0.886621189       0.0000       0.0000 0.0020
## [636,]   0.003110978758   0.155548938       0.0000       0.0000 0.0004
## [637,]  -0.034119827898   1.089285569       0.0000       0.0000 0.0024
## [638,]  -0.027586287285   1.709753842       0.0000       0.0000 0.0012
## [639,]   0.009966849736   0.410118400       0.0000       0.0000 0.0016
## [640,]  -0.105488693433   2.663842527       0.0000       0.0000 0.0032
## [641,]  -0.005135510457   0.354029314       0.0000       0.0000 0.0012
## [642,]  -0.640510290189   8.719694453       0.0000       0.0000 0.0080
## [643,]   0.361484644902   6.896079382       0.0000       0.0000 0.0036
## [644,]  -0.003489137480   0.447002294       0.0000       0.0000 0.0020
## [645,]  -0.005109810825   0.255490541       0.0000       0.0000 0.0004
## [646,]  -0.002286929002   0.709971694       0.0000       0.0000 0.0028
## [647,]  -0.010898382309   0.385607247       0.0000       0.0000 0.0020
## [648,]  -0.013898107209   0.674005366       0.0000       0.0000 0.0028
## [649,]  -0.009880247074   0.342066072       0.0000       0.0000 0.0012
## [650,]   0.010660517262   0.459402439       0.0000       0.0000 0.0008

3.2.4 Predict fitted values for each individual

pred.npb <- predict(fit.npb)
fittedvals <- pred.npb$fitted.vals

3.2.5 Plot predicted outcomes against “measured” outcomes

plot(fittedvals, Y)
abline(a = 0, b = 1, col = "red")

3.3 Run the NPB model with temperaure and ozone

Below I’ve used the set of priors labeled “24” and set scaleY = T

The priors are as follows: r priors.npb.24

Note that this version of the model does not include gest_age_w. It does include an indicator variable for season of conception (ref = winter) and the lon/lat as covariates and the percentage of the census tract population that is not NHW as an exposure.

priors.npb <- priors.npb.24

#' Exposures 
colnames(X.scaled)
##  [1] "mean_pm"             "mean_o3"             "mean_temp"          
##  [4] "pct_tree_cover"      "pct_impervious"      "mean_aadt_intensity"
##  [7] "dist_m_tri"          "dist_m_npl"          "dist_m_waste_site"  
## [10] "dist_m_major_emit"   "dist_m_cafo"         "dist_m_mine_well"   
## [13] "cvd_rate_adj"        "res_rate_adj"        "violent_crime_rate" 
## [16] "property_crime_rate" "pct_less_hs"         "pct_unemp"          
## [19] "pct_limited_eng"     "pct_hh_pov"          "pct_poc"
#' Covariates
colnames(W.scaled2)
##  [1] "lat"           "lon"           "lat_lon_int"   "ed_no_hs"     
##  [5] "ed_hs"         "ed_aa"         "ed_4yr"        "low_bmi"      
##  [9] "ovwt_bmi"      "obese_bmi"     "concep_spring" "concep_summer"
## [13] "concep_fall"   "concep_2010"   "concep_2011"   "concep_2012"  
## [17] "concep_2013"   "maternal_age"  "any_smoker"    "smokeSH"      
## [21] "mean_cpss"     "mean_epsd"     "male"
# fit.npb2 <- npb(niter = 5000, nburn = 2500, X = X.scaled, Y = Y, W = W.scaled2,
#                scaleY = TRUE,
#                priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb2, file = here::here("Results", "NPB_Birth_Weight_v4a.2.rdata"))

load(here::here("Results", "NPB_Birth_Weight_v4a.2.rdata"))
npb.sum2 <- summary(fit.npb2)

3.3.1 First, main effect regression coefficients with PIPs

rownames(npb.sum2$main.effects) <- colnames(X.scaled)
npb.sum2$main.effects
##                     Posterior Mean        SD 95% CI Lower 95% CI Upper    PIP
## mean_pm                 -6.4455763 14.489731    -51.36621     2.683216 0.3900
## mean_o3                -11.0042874 22.752166    -77.86027     2.341424 0.4668
## mean_temp               -1.0527040 21.370684    -31.95659    15.886379 0.3216
## pct_tree_cover          -2.0605910  6.449766    -19.12039     5.108510 0.2828
## pct_impervious          -2.9374980  7.398262    -25.44654     1.796266 0.3024
## mean_aadt_intensity     -0.8049048  5.433489    -14.31492     8.551697 0.2352
## dist_m_tri              -2.1739110  6.890125    -21.93467     6.114000 0.2940
## dist_m_npl              -0.9900659  5.268705    -14.29863     6.505562 0.2416
## dist_m_waste_site        0.4862897  7.223983    -11.84406    21.160154 0.2316
## dist_m_major_emit       -0.8789868  5.184028    -14.26873     8.054941 0.2276
## dist_m_cafo             -4.6180766 17.227018    -44.13164     9.197160 0.3720
## dist_m_mine_well        -2.9322838  8.180628    -26.42892     5.800016 0.3208
## cvd_rate_adj            -3.0336843  7.593749    -26.24958     4.104509 0.3336
## res_rate_adj            -3.6478780  8.345746    -28.46638     2.910625 0.3524
## violent_crime_rate      -1.0976867  5.955153    -15.26852     6.775785 0.2476
## property_crime_rate     -2.1636489  6.153787    -19.26523     4.354570 0.2876
## pct_less_hs             -3.1518381  8.226334    -26.93850     4.009727 0.3264
## pct_unemp              -15.7384162 21.089822    -73.05732     0.000000 0.6156
## pct_limited_eng         -2.5649220  7.175619    -23.53298     2.606821 0.2868
## pct_hh_pov              -2.5735162  7.067605    -22.47381     2.354691 0.2944
## pct_poc                 -2.6849906  8.157365    -25.36287     4.181035 0.3036

3.3.3 Interactions

Next, all of the interactions between exposures or between exposures and covariates

npb.sum2$interactions
##           Posterior Mean           SD 95% CI Lower 95% CI Upper    PIP
##   [1,]    1.194658926659   8.57711879      0.00000       0.0000 0.0216
##   [2,]    1.052533086230   8.03807503      0.00000       0.0000 0.0200
##   [3,]   -0.003185446482   0.92512170      0.00000       0.0000 0.0024
##   [4,]   -0.018234201891   0.52129268      0.00000       0.0000 0.0016
##   [5,]    0.014956771419   0.49698695      0.00000       0.0000 0.0012
##   [6,]   -0.004561501319   0.36148257      0.00000       0.0000 0.0028
##   [7,]   -0.018155212716   0.59266879      0.00000       0.0000 0.0020
##   [8,]   -0.012546584738   0.44681547      0.00000       0.0000 0.0016
##   [9,]   -0.016837852880   0.45595145      0.00000       0.0000 0.0036
##  [10,]   -0.042703830606   0.82466283      0.00000       0.0000 0.0036
##  [11,]    0.001608820602   0.34180533      0.00000       0.0000 0.0028
##  [12,]   -0.021844129742   0.56526999      0.00000       0.0000 0.0028
##  [13,]   -0.009765518433   0.39451776      0.00000       0.0000 0.0032
##  [14,]   -0.035696541157   0.77000573      0.00000       0.0000 0.0032
##  [15,]   -0.002621529365   0.27549081      0.00000       0.0000 0.0008
##  [16,]   -0.033604211639   0.78382068      0.00000       0.0000 0.0040
##  [17,]   -0.013301097351   0.42436228      0.00000       0.0000 0.0016
##  [18,]   -0.090105690587   1.69999876      0.00000       0.0000 0.0056
##  [19,]   -0.005049895956   0.19066975      0.00000       0.0000 0.0008
##  [20,]   -0.014803432043   0.67378729      0.00000       0.0000 0.0032
##  [21,] -171.586953546664  32.64089047   -241.01292    -120.2583 1.0000
##  [22,]   -0.013635922495   0.35496660      0.00000       0.0000 0.0020
##  [23,]   -0.012682016081   0.39454924      0.00000       0.0000 0.0016
##  [24,]   -0.003734548575   0.42229682      0.00000       0.0000 0.0012
##  [25,]   -0.029055286362   0.67199799      0.00000       0.0000 0.0028
##  [26,]   -0.018132591417   0.52436740      0.00000       0.0000 0.0016
##  [27,]   -0.113254844358   1.90957615      0.00000       0.0000 0.0052
##  [28,]   -0.006644755107   0.46889824      0.00000       0.0000 0.0016
##  [29,]   -0.009598516058   0.34205166      0.00000       0.0000 0.0008
##  [30,]   -0.034347717584   0.85181540      0.00000       0.0000 0.0028
##  [31,]    0.011819037075   0.56315276      0.00000       0.0000 0.0020
##  [32,]   -0.003461516042   0.20446331      0.00000       0.0000 0.0008
##  [33,]   -0.005769212102   0.18179199      0.00000       0.0000 0.0012
##  [34,]    0.000000000000   0.00000000      0.00000       0.0000 0.0000
##  [35,]    0.034329455299   1.02874325      0.00000       0.0000 0.0032
##  [36,]    0.032492362349   1.03409558      0.00000       0.0000 0.0016
##  [37,]    0.000891031862   0.08448097      0.00000       0.0000 0.0012
##  [38,]    0.090980960008   2.21371528      0.00000       0.0000 0.0028
##  [39,]   -0.010382011432   0.36864675      0.00000       0.0000 0.0020
##  [40,]   -0.016138476375   0.41620817      0.00000       0.0000 0.0024
##  [41,]   -0.009839010850   0.48059257      0.00000       0.0000 0.0012
##  [42,]    0.008104598286   0.22550419      0.00000       0.0000 0.0016
##  [43,]   -0.013429211899   0.57948800      0.00000       0.0000 0.0048
##  [44,]   -0.003394295259   0.28235672      0.00000       0.0000 0.0012
##  [45,]   -0.042573667130   0.95713794      0.00000       0.0000 0.0044
##  [46,]   -0.000826406587   0.40118896      0.00000       0.0000 0.0020
##  [47,]   -0.026966543148   0.75806092      0.00000       0.0000 0.0032
##  [48,]   -0.007680688178   0.21704419      0.00000       0.0000 0.0016
##  [49,]    0.008117026562   0.87097121      0.00000       0.0000 0.0020
##  [50,]    0.006346531419   0.38928508      0.00000       0.0000 0.0016
##  [51,]   -0.021299448942   0.55958888      0.00000       0.0000 0.0024
##  [52,]    0.013693274673   1.02422534      0.00000       0.0000 0.0016
##  [53,]    0.024996903348   1.08308278      0.00000       0.0000 0.0024
##  [54,]    0.018574679160   0.94261883      0.00000       0.0000 0.0016
##  [55,]   -0.024362560567   0.57485796      0.00000       0.0000 0.0028
##  [56,]    0.001678042324   0.37343646      0.00000       0.0000 0.0016
##  [57,]   -0.003953868511   0.16685696      0.00000       0.0000 0.0012
##  [58,]   -0.004799610070   0.25122579      0.00000       0.0000 0.0008
##  [59,]   -0.013293622476   0.55843588      0.00000       0.0000 0.0020
##  [60,]   -0.008947024374   0.54136289      0.00000       0.0000 0.0024
##  [61,]   -0.031357955854   1.06565322      0.00000       0.0000 0.0028
##  [62,]    0.015880659888   0.66992662      0.00000       0.0000 0.0024
##  [63,]    0.040153744116   1.67909645      0.00000       0.0000 0.0028
##  [64,]   -0.020421245428   0.54028258      0.00000       0.0000 0.0028
##  [65,]   -0.016600414772   0.40215708      0.00000       0.0000 0.0028
##  [66,]    0.000832641679   0.03198112      0.00000       0.0000 0.0012
##  [67,]    0.000313880310   0.13587445      0.00000       0.0000 0.0016
##  [68,]   -0.012904860091   0.33997237      0.00000       0.0000 0.0016
##  [69,]   -0.012906985427   0.37150742      0.00000       0.0000 0.0024
##  [70,]   -0.014995334410   0.45596885      0.00000       0.0000 0.0020
##  [71,]   -0.008608882464   0.46065656      0.00000       0.0000 0.0008
##  [72,]    0.003825531837   0.41208515      0.00000       0.0000 0.0008
##  [73,]    0.025834609207   0.76024914      0.00000       0.0000 0.0016
##  [74,]   -0.004848640804   0.19505860      0.00000       0.0000 0.0008
##  [75,]   -0.000423103699   0.66000525      0.00000       0.0000 0.0016
##  [76,]    0.007639130633   0.41240669      0.00000       0.0000 0.0028
##  [77,]    0.003876165318   0.59269436      0.00000       0.0000 0.0012
##  [78,]   -0.001811329169   0.31879677      0.00000       0.0000 0.0020
##  [79,]   -0.003734793780   0.18673969      0.00000       0.0000 0.0004
##  [80,]   -0.027933645383   0.68769370      0.00000       0.0000 0.0024
##  [81,]    0.002650860284   0.57650950      0.00000       0.0000 0.0024
##  [82,]   -0.016887597673   0.43320387      0.00000       0.0000 0.0016
##  [83,]   -0.019308661504   0.95671561      0.00000       0.0000 0.0020
##  [84,]    0.000330648547   0.14159500      0.00000       0.0000 0.0008
##  [85,]   -0.013388069237   0.51592470      0.00000       0.0000 0.0028
##  [86,]   -0.014441395277   0.51131969      0.00000       0.0000 0.0024
##  [87,]   -0.008416476950   0.26162437      0.00000       0.0000 0.0016
##  [88,]   -0.005732547922   0.20673934      0.00000       0.0000 0.0012
##  [89,]   -0.000857799082   0.05895210      0.00000       0.0000 0.0008
##  [90,]    0.000683600453   0.03418002      0.00000       0.0000 0.0004
##  [91,]    0.003851299075   0.38392497      0.00000       0.0000 0.0016
##  [92,]   -0.007454980732   0.41341438      0.00000       0.0000 0.0016
##  [93,]    0.015001946600   0.43997718      0.00000       0.0000 0.0016
##  [94,]    0.017991156456   0.70262373      0.00000       0.0000 0.0024
##  [95,]   -0.015076054331   0.73672139      0.00000       0.0000 0.0020
##  [96,]   -0.002107585358   0.14812449      0.00000       0.0000 0.0012
##  [97,]   -0.009268562489   0.38915641      0.00000       0.0000 0.0028
##  [98,]   -0.018475394186   0.49671920      0.00000       0.0000 0.0016
##  [99,]   -0.010059720923   0.41898146      0.00000       0.0000 0.0032
## [100,]   -0.022049857681   0.66317079      0.00000       0.0000 0.0024
## [101,]   -0.000393655823   0.34043129      0.00000       0.0000 0.0016
## [102,]   -0.015397807544   0.47746187      0.00000       0.0000 0.0020
## [103,]    0.001272539714   0.23593355      0.00000       0.0000 0.0016
## [104,]   -0.009892363892   0.59665144      0.00000       0.0000 0.0020
## [105,]    0.007747953187   0.33554846      0.00000       0.0000 0.0008
## [106,]   -0.004709086305   0.17474516      0.00000       0.0000 0.0008
## [107,]   -0.000460775722   0.44833311      0.00000       0.0000 0.0024
## [108,]   -0.004805551141   0.56405991      0.00000       0.0000 0.0020
## [109,]    0.001923025411   0.28114255      0.00000       0.0000 0.0024
## [110,]   -0.006284330981   0.35295907      0.00000       0.0000 0.0016
## [111,]    0.015440379558   1.07384143      0.00000       0.0000 0.0032
## [112,]    0.004602746801   0.56758717      0.00000       0.0000 0.0028
## [113,]   -0.017735981111   0.54082001      0.00000       0.0000 0.0012
## [114,]   -0.010477644173   0.35254096      0.00000       0.0000 0.0016
## [115,]   -0.004642558155   0.13795289      0.00000       0.0000 0.0020
## [116,]    0.033984364493   1.00079740      0.00000       0.0000 0.0016
## [117,]    0.005451446967   0.58457171      0.00000       0.0000 0.0020
## [118,]    0.035349518956   1.06691479      0.00000       0.0000 0.0020
## [119,]   -0.003648434595   0.50870251      0.00000       0.0000 0.0020
## [120,]   -0.000406517433   0.55694524      0.00000       0.0000 0.0036
## [121,]   -0.000963162730   0.04815814      0.00000       0.0000 0.0004
## [122,]   -0.010886914652   0.29603307      0.00000       0.0000 0.0020
## [123,]   -0.004181084324   0.20905422      0.00000       0.0000 0.0004
## [124,]   -0.002813651968   0.15860679      0.00000       0.0000 0.0016
## [125,]    0.002412117795   0.07549225      0.00000       0.0000 0.0012
## [126,]    0.001875640973   0.22705145      0.00000       0.0000 0.0008
## [127,]    0.008956258568   0.42606253      0.00000       0.0000 0.0016
## [128,]   -0.005605121654   0.31091848      0.00000       0.0000 0.0008
## [129,]   -0.021503640232   0.60632185      0.00000       0.0000 0.0020
## [130,]    0.003476714569   0.53826125      0.00000       0.0000 0.0024
## [131,]   -0.008225512205   0.33395428      0.00000       0.0000 0.0024
## [132,]   -0.007732973710   0.27364489      0.00000       0.0000 0.0008
## [133,]    0.006951429732   0.25371934      0.00000       0.0000 0.0024
## [134,]    0.029619931657   1.19228010      0.00000       0.0000 0.0028
## [135,]   -0.005366327000   0.50851184      0.00000       0.0000 0.0020
## [136,]   -0.000776080663   0.05100858      0.00000       0.0000 0.0008
## [137,]   -0.001577414046   0.07887070      0.00000       0.0000 0.0004
## [138,]   -0.000891178314   0.21133029      0.00000       0.0000 0.0012
## [139,]   -0.000002495391   0.18025979      0.00000       0.0000 0.0008
## [140,]   -0.009682510062   0.43161588      0.00000       0.0000 0.0028
## [141,]   -0.004192803302   0.24446649      0.00000       0.0000 0.0024
## [142,]   -0.008893544472   0.30999501      0.00000       0.0000 0.0016
## [143,]    0.006367943894   0.24943255      0.00000       0.0000 0.0008
## [144,]   -0.000945586753   0.08585128      0.00000       0.0000 0.0012
## [145,]    0.088491677927   1.94253998      0.00000       0.0000 0.0044
## [146,]    0.150700722299   2.74476634      0.00000       0.0000 0.0048
## [147,]   -0.017597788805   0.40711579      0.00000       0.0000 0.0036
## [148,]   -0.003780226209   0.17330904      0.00000       0.0000 0.0012
## [149,]   -0.022814248872   0.57874353      0.00000       0.0000 0.0028
## [150,]   -0.008452353163   0.42024664      0.00000       0.0000 0.0012
## [151,]   -0.008477136934   0.33429740      0.00000       0.0000 0.0012
## [152,]   -0.021673574084   0.52291745      0.00000       0.0000 0.0020
## [153,]   -0.028821327022   1.01500062      0.00000       0.0000 0.0024
## [154,]   -0.002385981880   0.26125699      0.00000       0.0000 0.0016
## [155,]   -0.023793618732   0.58868240      0.00000       0.0000 0.0020
## [156,]   -0.013030076973   0.56096188      0.00000       0.0000 0.0032
## [157,]   -0.032063508430   0.86222752      0.00000       0.0000 0.0024
## [158,]   -0.006928029894   0.22231287      0.00000       0.0000 0.0012
## [159,]   -0.018003360539   0.63679968      0.00000       0.0000 0.0036
## [160,]   -0.017866553094   0.50354458      0.00000       0.0000 0.0028
## [161,]    0.029489019057   1.25936133      0.00000       0.0000 0.0020
## [162,]   -0.004526034420   0.22629083      0.00000       0.0000 0.0016
## [163,]    0.041483487215   1.51062485      0.00000       0.0000 0.0028
## [164,]   -0.006481527125   0.49159316      0.00000       0.0000 0.0024
## [165,]    0.013752331880   0.59521771      0.00000       0.0000 0.0012
## [166,]   -0.008404552944   0.36900719      0.00000       0.0000 0.0008
## [167,]    0.001653312193   0.32728851      0.00000       0.0000 0.0028
## [168,]   -0.001716277654   0.29694072      0.00000       0.0000 0.0016
## [169,]   -0.010367244994   0.37112010      0.00000       0.0000 0.0016
## [170,]    0.011986728949   0.56161748      0.00000       0.0000 0.0028
## [171,]    0.037807663064   1.24540099      0.00000       0.0000 0.0040
## [172,]    0.299287118402   4.61361295      0.00000       0.0000 0.0084
## [173,]    0.090529864815   2.10657910      0.00000       0.0000 0.0040
## [174,]    0.118577108328   2.40921839      0.00000       0.0000 0.0040
## [175,]   -0.024176733638   0.67818526      0.00000       0.0000 0.0024
## [176,]   -0.005597761596   0.41679394      0.00000       0.0000 0.0016
## [177,]   -0.024496151559   0.69993725      0.00000       0.0000 0.0024
## [178,]   -0.013629272319   0.45167395      0.00000       0.0000 0.0020
## [179,]   -0.035317539233   0.68003494      0.00000       0.0000 0.0044
## [180,]   -0.012725301588   0.47708349      0.00000       0.0000 0.0012
## [181,]   -0.030118243790   0.92107450      0.00000       0.0000 0.0020
## [182,]   -0.018255305252   0.70075519      0.00000       0.0000 0.0040
## [183,]   -0.006840298588   0.31510806      0.00000       0.0000 0.0012
## [184,]   -0.022523122033   0.69788990      0.00000       0.0000 0.0032
## [185,]   -0.005265965802   0.20179566      0.00000       0.0000 0.0008
## [186,]   -0.001143731197   0.05718656      0.00000       0.0000 0.0004
## [187,]    0.000559862366   0.56973077      0.00000       0.0000 0.0024
## [188,]   -0.013303727509   0.47145534      0.00000       0.0000 0.0012
## [189,]   -0.006708749833   0.19591764      0.00000       0.0000 0.0016
## [190,]   -0.001701940981   0.06045628      0.00000       0.0000 0.0008
## [191,]    0.000551109493   0.02730120      0.00000       0.0000 0.0008
## [192,]   -0.009289596366   0.30240878      0.00000       0.0000 0.0020
## [193,]   -0.016135968891   0.65838643      0.00000       0.0000 0.0016
## [194,]    0.000000000000   0.00000000      0.00000       0.0000 0.0000
## [195,]   -0.004854667948   0.36093531      0.00000       0.0000 0.0028
## [196,]    0.006554430648   0.40516775      0.00000       0.0000 0.0012
## [197,]   -0.019250736252   0.57157752      0.00000       0.0000 0.0024
## [198,]   -0.007039123593   0.39115934      0.00000       0.0000 0.0028
## [199,]    0.009290034578   0.31297712      0.00000       0.0000 0.0012
## [200,]   -0.001758301228   0.18134508      0.00000       0.0000 0.0016
## [201,]   -0.003977026075   0.23062606      0.00000       0.0000 0.0008
## [202,]   -0.008781514878   0.35862958      0.00000       0.0000 0.0016
## [203,]    0.005422113089   0.43443853      0.00000       0.0000 0.0024
## [204,]    0.001298488325   0.54206200      0.00000       0.0000 0.0024
## [205,]   -0.045140605106   0.80979727      0.00000       0.0000 0.0044
## [206,]   -0.002463679682   0.40522679      0.00000       0.0000 0.0028
## [207,]   -0.024193304664   0.61816896      0.00000       0.0000 0.0032
## [208,]   -0.000726262595   0.36035922      0.00000       0.0000 0.0016
## [209,]   -0.005220112807   0.49509767      0.00000       0.0000 0.0012
## [210,]   -0.005193507157   0.18478067      0.00000       0.0000 0.0012
## [211,]    0.027562778639   1.01252271      0.00000       0.0000 0.0016
## [212,]   -0.001038545268   0.24867210      0.00000       0.0000 0.0016
## [213,]   -0.011736363032   0.66030986      0.00000       0.0000 0.0024
## [214,]   -0.021543431781   0.52616493      0.00000       0.0000 0.0028
## [215,]   -0.013748384918   0.37747431      0.00000       0.0000 0.0016
## [216,]   -0.022944009673   0.68944723      0.00000       0.0000 0.0028
## [217,]    0.017200109542   1.13877714      0.00000       0.0000 0.0020
## [218,]   -0.527485930285   9.42884150      0.00000       0.0000 0.0052
## [219,]   -0.061472957291   1.82372752      0.00000       0.0000 0.0020
## [220,]    0.000596598768   0.26777878      0.00000       0.0000 0.0012
## [221,]    0.023582937270   1.24305860      0.00000       0.0000 0.0024
## [222,]   -0.016449272520   0.83668664      0.00000       0.0000 0.0032
## [223,]   -0.822750123029  11.23793845      0.00000       0.0000 0.0068
## [224,]   -0.153954912213   5.75957412      0.00000       0.0000 0.0032
## [225,]   -0.013637763790   0.52133528      0.00000       0.0000 0.0020
## [226,]    0.296140141503   6.45227980      0.00000       0.0000 0.0028
## [227,]   -0.481673714272   8.12712883      0.00000       0.0000 0.0068
## [228,]    0.001319222524   0.47523532      0.00000       0.0000 0.0016
## [229,]   -0.477882614440   8.39962387      0.00000       0.0000 0.0052
## [230,]   -0.022074450913   1.06459354      0.00000       0.0000 0.0036
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## [235,]    0.003955584846   0.12769615      0.00000       0.0000 0.0012
## [236,]   -0.023176418306   0.65444573      0.00000       0.0000 0.0032
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## [244,]   -0.018651301472   1.98110757      0.00000       0.0000 0.0036
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## [246,]   -6.381064999170  38.61721953   -165.07908       0.0000 0.0292
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## [268,] -109.252843015111 115.81264483   -367.31384       0.0000 0.5200
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## [270,]   -0.131106221668   4.31891546      0.00000       0.0000 0.0032
## [271,]   -0.160657366081   4.31515803      0.00000       0.0000 0.0032
## [272,]   49.810838060870  72.54306207      0.00000     202.6349 0.3472
## [273,]   -0.403869600075   7.73474288      0.00000       0.0000 0.0036
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## [290,]   -0.010790692539   0.38580003      0.00000       0.0000 0.0024
## [291,]   -0.025134196377   0.54233648      0.00000       0.0000 0.0032
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## [293,]   -0.001036430824   1.54306312      0.00000       0.0000 0.0024
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## [296,]   -0.010178590269   0.37967656      0.00000       0.0000 0.0020
## [297,]   -0.002682792021   0.91222713      0.00000       0.0000 0.0032
## [298,]    0.024444168637   1.76530537      0.00000       0.0000 0.0032
## [299,]    0.007990055093   0.29286973      0.00000       0.0000 0.0016
## [300,]   -0.001627917128   0.08014360      0.00000       0.0000 0.0008
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## [305,]   -0.024236515622   0.56653345      0.00000       0.0000 0.0032
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## [307,]   -0.007705804987   0.24731681      0.00000       0.0000 0.0016
## [308,]   -0.050101991722   1.17559093      0.00000       0.0000 0.0032
## [309,]    0.001415322569   0.58685220      0.00000       0.0000 0.0032
## [310,]   -0.776385119815  11.30226364      0.00000       0.0000 0.0072
## [311,]   -0.000876579143   0.38300705      0.00000       0.0000 0.0024
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## [313,]   -0.011275117677   0.65344592      0.00000       0.0000 0.0028
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## [474,]   -0.020932029419   0.97361159      0.00000       0.0000 0.0016
## [475,]   -0.052953905210   2.00074101      0.00000       0.0000 0.0028
## [476,]    0.151992585969   3.75062811      0.00000       0.0000 0.0040
## [477,]   -0.020712380672   0.58198882      0.00000       0.0000 0.0036
## [478,]    0.201725984480   3.89929412      0.00000       0.0000 0.0052
## [479,]   -0.944665659700  10.20953518      0.00000       0.0000 0.0144
## [480,]    0.007191279594   0.77566688      0.00000       0.0000 0.0016
## [481,]   -0.004747201506   0.37765055      0.00000       0.0000 0.0016
## [482,]    0.000000000000   0.00000000      0.00000       0.0000 0.0000
## [483,]   -0.002946473785   1.54190799      0.00000       0.0000 0.0032
## [484,]    0.022016929999   0.67156219      0.00000       0.0000 0.0016
## [485,]    0.019550831825   0.75910631      0.00000       0.0000 0.0028
## [486,]   -0.019922180007   0.49152646      0.00000       0.0000 0.0020
## [487,]   -0.012014219659   0.40171736      0.00000       0.0000 0.0016
## [488,]   -0.000702300859   0.39415527      0.00000       0.0000 0.0012
## [489,]   -0.031895048562   0.76733243      0.00000       0.0000 0.0036
## [490,]   -0.237150755292   5.58797907      0.00000       0.0000 0.0032
## [491,]   -0.025206163428   0.69404641      0.00000       0.0000 0.0032
## [492,]    0.031266663133   1.03477366      0.00000       0.0000 0.0028
## [493,]   -0.015002003469   0.71364340      0.00000       0.0000 0.0024
## [494,]   -0.091823265998   3.77325851      0.00000       0.0000 0.0028
## [495,]    0.115514467870   3.18744884      0.00000       0.0000 0.0024
## [496,]    0.007073058362   1.08701403      0.00000       0.0000 0.0048
## [497,]   -0.059984249106   2.06609558      0.00000       0.0000 0.0024
## [498,]    0.013380802964   0.70266338      0.00000       0.0000 0.0020
## [499,]   -0.311417468699   5.86930203      0.00000       0.0000 0.0060
## [500,]   -0.082466726430   3.05199849      0.00000       0.0000 0.0036
## [501,]   -0.063481670579   2.22003665      0.00000       0.0000 0.0040
## [502,]    0.695874345943   7.84151553      0.00000       0.0000 0.0100
## [503,]   -0.077987062658   3.04114290      0.00000       0.0000 0.0024
## [504,]    0.000534241268   0.11011044      0.00000       0.0000 0.0008
## [505,]   -0.177625395811   4.56253794      0.00000       0.0000 0.0028
## [506,]   -0.008990792877   1.16045339      0.00000       0.0000 0.0048
## [507,]    0.007480325094   0.35285439      0.00000       0.0000 0.0020
## [508,]   -0.003706506523   0.31151956      0.00000       0.0000 0.0020
## [509,]    0.019858965863   0.86004112      0.00000       0.0000 0.0024
## [510,]   -0.007113525954   0.31026457      0.00000       0.0000 0.0024
## [511,]   -0.023789796940   0.47992429      0.00000       0.0000 0.0036
## [512,]   -0.007001337981   0.46222065      0.00000       0.0000 0.0024
## [513,]    0.035372343804   1.85952343      0.00000       0.0000 0.0016
## [514,]   -0.041146325063   1.16675472      0.00000       0.0000 0.0048
## [515,]    0.024569894807   1.17733959      0.00000       0.0000 0.0028
## [516,]   -0.038729259007   0.79540038      0.00000       0.0000 0.0040
## [517,]   -2.433917445470  20.39600088      0.00000       0.0000 0.0184
## [518,]    0.064121285559   2.88101757      0.00000       0.0000 0.0032
## [519,]    0.018263379964   0.97413938      0.00000       0.0000 0.0012
## [520,]   -0.046374988856   2.12109152      0.00000       0.0000 0.0032
## [521,]    0.019624279084   0.97706591      0.00000       0.0000 0.0016
## [522,]   -0.011509923230   0.80233647      0.00000       0.0000 0.0020
## [523,]   -0.295741831421   6.03023327      0.00000       0.0000 0.0040
## [524,]   -0.071756357074   2.29367832      0.00000       0.0000 0.0040
## [525,]    0.486339056075   7.38047615      0.00000       0.0000 0.0068
## [526,]   -0.024909991662   1.45920451      0.00000       0.0000 0.0032
## [527,]    0.000668505279   0.20791983      0.00000       0.0000 0.0012
## [528,]   -0.074893451055   4.15189534      0.00000       0.0000 0.0048
## [529,]   -0.002959047112   0.15611912      0.00000       0.0000 0.0016
## [530,]   -0.009701181462   0.39617506      0.00000       0.0000 0.0016
## [531,]    0.000964331227   0.37021534      0.00000       0.0000 0.0008
## [532,]   -0.021085388202   0.66425305      0.00000       0.0000 0.0020
## [533,]   -0.016588308276   0.46406294      0.00000       0.0000 0.0016
## [534,]   -0.015761447434   0.74048153      0.00000       0.0000 0.0036
## [535,]   -0.033641666084   0.80865479      0.00000       0.0000 0.0028
## [536,]   -0.353374998870   7.27765256      0.00000       0.0000 0.0040
## [537,]   -0.009732151221   0.40505174      0.00000       0.0000 0.0024
## [538,]    0.004064849735   0.39721265      0.00000       0.0000 0.0028
## [539,]   -0.047808513103   2.57291933      0.00000       0.0000 0.0040
## [540,]   -3.149816346975  24.35629563      0.00000       0.0000 0.0188
## [541,]    0.031170465180   1.41846291      0.00000       0.0000 0.0024
## [542,]    0.041501289371   1.59875284      0.00000       0.0000 0.0024
## [543,]   -0.007193706809   0.31029582      0.00000       0.0000 0.0016
## [544,]    0.050130758136   1.89778564      0.00000       0.0000 0.0024
## [545,]   -0.001609688718   0.32771696      0.00000       0.0000 0.0012
## [546,]   -0.042060005019   1.65104103      0.00000       0.0000 0.0024
## [547,]   -0.090028980636   2.71383231      0.00000       0.0000 0.0040
## [548,]    0.072214673699   1.83472644      0.00000       0.0000 0.0028
## [549,]    0.015448189250   1.12489852      0.00000       0.0000 0.0024
## [550,]    0.002357509643   0.11787548      0.00000       0.0000 0.0004
## [551,]   -0.615342276358  10.27247843      0.00000       0.0000 0.0064
## [552,]    0.004902521717   0.61534441      0.00000       0.0000 0.0032
## [553,]   -0.061780393401   1.18512139      0.00000       0.0000 0.0048
## [554,]   -0.010033060942   0.43739222      0.00000       0.0000 0.0020
## [555,]   -0.015707341482   0.49745682      0.00000       0.0000 0.0016
## [556,]    0.019120809008   0.93727996      0.00000       0.0000 0.0028
## [557,]    0.002148851716   0.10856103      0.00000       0.0000 0.0012
## [558,]   -0.001418855727   0.26168521      0.00000       0.0000 0.0016
## [559,]    0.279195775802   6.85445542      0.00000       0.0000 0.0048
## [560,]    0.006324499072   0.58796319      0.00000       0.0000 0.0024
## [561,]   -0.018359567141   0.79702743      0.00000       0.0000 0.0032
## [562,]   -0.008187370215   0.24256582      0.00000       0.0000 0.0020
## [563,]   -4.893557506878  30.88873618   -113.68021       0.0000 0.0280
## [564,]   -0.027306301264   0.53315093      0.00000       0.0000 0.0040
## [565,]    0.026129450817   1.46586026      0.00000       0.0000 0.0016
## [566,]    0.033878443039   1.91837361      0.00000       0.0000 0.0044
## [567,]   -0.010587412873   0.41549000      0.00000       0.0000 0.0016
## [568,]    0.000546002185   0.02730011      0.00000       0.0000 0.0004
## [569,]   -0.005350443023   0.57947771      0.00000       0.0000 0.0016
## [570,]   -0.005683310437   0.26922936      0.00000       0.0000 0.0012
## [571,]    0.031192268893   1.67329038      0.00000       0.0000 0.0020
## [572,]   -0.082289642035   2.71745019      0.00000       0.0000 0.0024
## [573,]   -0.007408078335   0.57225680      0.00000       0.0000 0.0020
## [574,]    0.101468059960   4.06389362      0.00000       0.0000 0.0028
## [575,]   -0.014803061619   0.42015444      0.00000       0.0000 0.0016
## [576,]   -0.038157398462   0.96771472      0.00000       0.0000 0.0028
## [577,]   -0.016838153982   0.62606940      0.00000       0.0000 0.0012
## [578,]   -0.051206337381   1.36715704      0.00000       0.0000 0.0028
## [579,]    0.017431100643   1.12300694      0.00000       0.0000 0.0028
## [580,]   -0.015705955501   0.47194817      0.00000       0.0000 0.0028
## [581,]   -0.005823385442   1.04493642      0.00000       0.0000 0.0024
## [582,]   -0.008327191849   0.26997707      0.00000       0.0000 0.0016
## [583,]   -0.008224004069   0.51365716      0.00000       0.0000 0.0020
## [584,]    0.000293044734   0.12988490      0.00000       0.0000 0.0012
## [585,]   -0.176997796867   4.08528311      0.00000       0.0000 0.0044
## [586,]   -0.075577285608   7.60214903      0.00000       0.0000 0.0048
## [587,]    0.119888154992   3.42371234      0.00000       0.0000 0.0028
## [588,]   -0.007799685570   0.38998428      0.00000       0.0000 0.0004
## [589,]   -0.010990006471   0.40310680      0.00000       0.0000 0.0016
## [590,]   -0.002150097747   0.09175791      0.00000       0.0000 0.0008
## [591,]   -0.073865496276   3.00026361      0.00000       0.0000 0.0044
## [592,]    0.006153834111   0.46561152      0.00000       0.0000 0.0012
## [593,]   -0.130458970258   4.49840117      0.00000       0.0000 0.0024
## [594,]    0.122847692267   3.01441291      0.00000       0.0000 0.0044
## [595,]   -0.176540088771   4.36019213      0.00000       0.0000 0.0052
## [596,]   -0.016558233794   0.47873279      0.00000       0.0000 0.0012
## [597,]   -0.024115516629   0.75122837      0.00000       0.0000 0.0028
## [598,]    0.015248573081   0.81070768      0.00000       0.0000 0.0024
## [599,]   -0.004214301891   0.15025325      0.00000       0.0000 0.0008
## [600,]   -0.008176933522   0.29975618      0.00000       0.0000 0.0008
## [601,]   -0.031496691082   0.69013981      0.00000       0.0000 0.0036
## [602,]    0.004500005844   0.89306130      0.00000       0.0000 0.0032
## [603,]   -0.032022029851   0.68385097      0.00000       0.0000 0.0040
## [604,]   -0.020249888036   0.88381822      0.00000       0.0000 0.0024
## [605,]   -0.019820427618   0.67765017      0.00000       0.0000 0.0024
## [606,]   -0.012412917909   0.45167745      0.00000       0.0000 0.0012
## [607,]   -0.041197911184   1.08770050      0.00000       0.0000 0.0040
## [608,]   -1.587592822426  14.96744371      0.00000       0.0000 0.0136
## [609,]   -0.387919566458   8.00542416      0.00000       0.0000 0.0052
## [610,]   -0.080293402392   2.61165725      0.00000       0.0000 0.0028
## [611,]   -0.001558608453   0.31393656      0.00000       0.0000 0.0016
## [612,]   -0.022352226102   0.75711186      0.00000       0.0000 0.0032
## [613,]    0.015325554656   1.18397379      0.00000       0.0000 0.0008
## [614,]   -0.154410384103   3.91033403      0.00000       0.0000 0.0044
## [615,]   -0.013927183637   1.26685015      0.00000       0.0000 0.0040
## [616,]   -0.505878481684   8.12830958      0.00000       0.0000 0.0068
## [617,]    0.002436891997   0.47225124      0.00000       0.0000 0.0008
## [618,]   -0.009043554156   0.32143329      0.00000       0.0000 0.0008
## [619,]   -0.027725441885   0.80890839      0.00000       0.0000 0.0040
## [620,]   -0.532255547964   8.76815556      0.00000       0.0000 0.0068
## [621,]   -0.460934550168   6.96439907      0.00000       0.0000 0.0068
## [622,]   -0.006410519595   0.19181560      0.00000       0.0000 0.0016
## [623,]   -0.001669547557   0.12147308      0.00000       0.0000 0.0016
## [624,]   -0.303647690130   5.19002738      0.00000       0.0000 0.0068
## [625,]   -0.030274780092   0.88364558      0.00000       0.0000 0.0036
## [626,]   -0.004875335079   0.20808248      0.00000       0.0000 0.0012
## [627,]   -0.009676559227   0.36391025      0.00000       0.0000 0.0016
## [628,]   -0.005437744653   0.36327706      0.00000       0.0000 0.0012
## [629,]   -0.019389612318   0.50678962      0.00000       0.0000 0.0028
## [630,]   -0.012288045516   0.68869913      0.00000       0.0000 0.0028
## [631,]   -0.059112392740   2.66714733      0.00000       0.0000 0.0020
## [632,]   -0.215563662485   5.43283801      0.00000       0.0000 0.0024
## [633,]    0.023601764614   1.23041497      0.00000       0.0000 0.0016
## [634,]    0.041090833667   1.20202927      0.00000       0.0000 0.0024
## [635,]   -0.028098901482   1.12866358      0.00000       0.0000 0.0036
## [636,]   -0.017087319670   0.43078305      0.00000       0.0000 0.0028
## [637,]   -0.001841458162   0.16875590      0.00000       0.0000 0.0008
## [638,]    0.039488977937   1.90753564      0.00000       0.0000 0.0036
## [639,]   -0.296715074766   6.57656642      0.00000       0.0000 0.0044
## [640,]    0.058721821789   1.49050057      0.00000       0.0000 0.0024
## [641,]   -0.036070870827   1.02481991      0.00000       0.0000 0.0036
## [642,]    0.002557239633   0.33352639      0.00000       0.0000 0.0024
## [643,]   -0.437462914987   9.07755990      0.00000       0.0000 0.0048
## [644,]    0.006683288095   1.12666540      0.00000       0.0000 0.0032
## [645,]   -0.018481701973   0.41662465      0.00000       0.0000 0.0036
## [646,]   -0.008238724999   0.30220433      0.00000       0.0000 0.0024
## [647,]   -0.002712076393   0.46671843      0.00000       0.0000 0.0016
## [648,]    0.026182066976   1.42404472      0.00000       0.0000 0.0040
## [649,]   -0.021680874636   0.63284376      0.00000       0.0000 0.0036
## [650,]   -0.018352899312   0.76942640      0.00000       0.0000 0.0016
## [651,]    0.001598953523   0.31296010      0.00000       0.0000 0.0016
## [652,]    0.006360029744   0.26786101      0.00000       0.0000 0.0012
## [653,]    0.000360548225   0.53151130      0.00000       0.0000 0.0020
## [654,]   -0.000991394423   0.70114703      0.00000       0.0000 0.0024
## [655,]   -0.562551393117  10.60018792      0.00000       0.0000 0.0068
## [656,]   -0.008531306138   0.56394670      0.00000       0.0000 0.0012
## [657,]    0.047274460945   2.40919357      0.00000       0.0000 0.0016
## [658,]   -0.000128555301   0.28776775      0.00000       0.0000 0.0008
## [659,]   -0.003734793780   0.18673969      0.00000       0.0000 0.0004
## [660,]   -0.041314290532   2.52951024      0.00000       0.0000 0.0020
## [661,]   -0.004745669618   0.41900631      0.00000       0.0000 0.0020
## [662,]   -0.172083902754   4.22895772      0.00000       0.0000 0.0036
## [663,]    1.857876545623  14.60144737      0.00000       0.0000 0.0196
## [664,]   -0.084554333375   2.78749175      0.00000       0.0000 0.0036
## [665,]   -0.023119395121   0.59717518      0.00000       0.0000 0.0024
## [666,]   -0.271402511477   6.68853848      0.00000       0.0000 0.0036
## [667,]   -0.030992435446   1.16477586      0.00000       0.0000 0.0032
## [668,]   -0.029434482769   0.81915857      0.00000       0.0000 0.0024
## [669,]    0.000619833068   0.27786346      0.00000       0.0000 0.0016
## [670,]   -0.036192665774   1.25579266      0.00000       0.0000 0.0036
## [671,]    0.004355016266   0.15986021      0.00000       0.0000 0.0012
## [672,]   -0.045662222311   1.05443324      0.00000       0.0000 0.0024
## [673,]   -0.005766744226   0.28943464      0.00000       0.0000 0.0016
## [674,]   -0.122694864749   5.03176032      0.00000       0.0000 0.0052
## [675,]   -0.003623059359   0.14930229      0.00000       0.0000 0.0008
## [676,]    0.005100179164   0.48618083      0.00000       0.0000 0.0008
## [677,]   -0.016934522868   0.82640121      0.00000       0.0000 0.0012
## [678,]   -0.212541452931   5.07587170      0.00000       0.0000 0.0052
## [679,]    0.062386183715   1.89433837      0.00000       0.0000 0.0020
## [680,]   -0.027827543352   0.86711423      0.00000       0.0000 0.0028
## [681,]    0.002554967487   0.31854666      0.00000       0.0000 0.0012
## [682,]    0.089270982890   2.17937871      0.00000       0.0000 0.0032
## [683,]   -0.035426053547   0.85706951      0.00000       0.0000 0.0024
## [684,]    0.004567504779   0.67764079      0.00000       0.0000 0.0020
## [685,]   -1.754547128681  15.22012268      0.00000       0.0000 0.0156
## [686,]    1.653403614093  13.90185621      0.00000       0.0000 0.0188
## [687,]   -0.068474491864   2.52800112      0.00000       0.0000 0.0028
## [688,]    0.001661340212   0.36765531      0.00000       0.0000 0.0024
## [689,]   -0.182967651174   5.65166770      0.00000       0.0000 0.0036
## [690,]   -0.008267804300   0.59744544      0.00000       0.0000 0.0032
## [691,]   -0.015746654977   0.50950701      0.00000       0.0000 0.0020
## [692,]   -0.008984176592   0.28700121      0.00000       0.0000 0.0012
## [693,]   -0.012934723969   0.40373791      0.00000       0.0000 0.0016

3.3.4 Predict fitted values for each individual

pred.npb2 <- predict(fit.npb2)
fittedvals2 <- pred.npb2$fitted.vals

3.3.5 Plot predicted outcomes against “measured” outcomes

plot(fittedvals2, Y)
abline(a = 0, b = 1, col = "red")

3.4 Fit the NPB model without ozone and with temperature

Only ozone shows up in the NPB model. However, there is some speculation that ozone is just a proxy for some of the other variables. Here I am running the NPB model without ozone but with temperature just to see if something else pops up instead.

priors.npb <- priors.npb.24

#' Exposures
colnames(X.scaled)
##  [1] "mean_pm"             "mean_o3"             "mean_temp"          
##  [4] "pct_tree_cover"      "pct_impervious"      "mean_aadt_intensity"
##  [7] "dist_m_tri"          "dist_m_npl"          "dist_m_waste_site"  
## [10] "dist_m_major_emit"   "dist_m_cafo"         "dist_m_mine_well"   
## [13] "cvd_rate_adj"        "res_rate_adj"        "violent_crime_rate" 
## [16] "property_crime_rate" "pct_less_hs"         "pct_unemp"          
## [19] "pct_limited_eng"     "pct_hh_pov"          "pct_poc"
#' Covariates
colnames(W.scaled2)
##  [1] "lat"           "lon"           "lat_lon_int"   "ed_no_hs"     
##  [5] "ed_hs"         "ed_aa"         "ed_4yr"        "low_bmi"      
##  [9] "ovwt_bmi"      "obese_bmi"     "concep_spring" "concep_summer"
## [13] "concep_fall"   "concep_2010"   "concep_2011"   "concep_2012"  
## [17] "concep_2013"   "maternal_age"  "any_smoker"    "smokeSH"      
## [21] "mean_cpss"     "mean_epsd"     "male"
# fit.npb3 <- npb(niter = 5000, nburn = 2500, X = X.scaled[,-c(2)], Y = Y, W = W.scaled2,
#                 scaleY = TRUE,
#                 priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb3, file = here::here("Results", "NPB_Birth_Weight_v4a.3.rdata"))

load(here::here("Results", "NPB_Birth_Weight_v4a.3.rdata"))
npb.sum3 <- summary(fit.npb3)

3.4.1 First, main effect regression coefficients with PIPs

rownames(npb.sum3$main.effects) <- colnames(X.scaled[,-c(2)])
npb.sum3$main.effects
##                     Posterior Mean        SD 95% CI Lower 95% CI Upper    PIP
## mean_pm                 -6.2270028 11.829903    -40.83325    1.3329720 0.4216
## mean_temp               -5.9078416 14.521641    -48.41181    3.9188396 0.3936
## pct_tree_cover          -1.9400109  6.176479    -18.85633    5.1386887 0.2768
## pct_impervious          -3.8993339  8.193060    -28.11322    0.6778887 0.3512
## mean_aadt_intensity     -1.2645979  5.587482    -15.30176    6.5179151 0.2332
## dist_m_tri              -1.8403906  7.008697    -21.51611    9.4004148 0.2732
## dist_m_npl              -0.6330595  6.362851    -15.29715   12.8578425 0.2448
## dist_m_waste_site       -0.4297864  6.516643    -14.28281   13.9915356 0.2332
## dist_m_major_emit       -0.5368893  6.054691    -13.79800   11.8574575 0.2272
## dist_m_cafo             -3.3788146 13.135915    -32.52030    8.8764179 0.3396
## dist_m_mine_well        -4.9812807 10.496138    -35.19974    2.8591574 0.3868
## cvd_rate_adj            -4.0803243  9.027007    -29.75359    2.0091130 0.3660
## res_rate_adj            -4.6358931  9.454517    -31.85015    1.8292630 0.3928
## violent_crime_rate      -1.1196381  6.014000    -16.29494    7.4135878 0.2476
## property_crime_rate     -2.1919509  6.251015    -18.80068    2.8857337 0.2760
## pct_less_hs             -2.9564607  7.425378    -24.09712    4.3310094 0.3324
## pct_unemp              -12.3136410 17.898237    -62.01418    0.0000000 0.5756
## pct_limited_eng         -2.4849233  7.052612    -21.98537    3.2781220 0.2932
## pct_hh_pov              -2.2683344  6.679594    -19.73307    4.6395661 0.2964
## pct_poc                 -3.0137492  7.665084    -25.22988    3.7484350 0.3180

3.4.3 Interactions

Next, all of the interactions between exposures or between exposures and covariates

npb.sum3$interactions
##           Posterior Mean          SD 95% CI Lower 95% CI Upper    PIP
##   [1,]   -0.000376303369  0.25387243       0.0000       0.0000 0.0024
##   [2,]   -0.006764598353  0.33397270       0.0000       0.0000 0.0024
##   [3,]   -0.006935068553  0.22970068       0.0000       0.0000 0.0020
##   [4,]    0.015805756547  0.60557707       0.0000       0.0000 0.0012
##   [5,]   -0.006043426468  0.17538887       0.0000       0.0000 0.0012
##   [6,]    0.001295340895  0.45616661       0.0000       0.0000 0.0028
##   [7,]   -0.017682733203  0.43962863       0.0000       0.0000 0.0024
##   [8,]   -0.007409563610  0.57893001       0.0000       0.0000 0.0060
##   [9,]   -0.019516770679  0.47299718       0.0000       0.0000 0.0028
##  [10,]   -0.013874626769  0.33988058       0.0000       0.0000 0.0032
##  [11,]   -0.011215927711  0.30262510       0.0000       0.0000 0.0028
##  [12,]   -0.017190382562  0.63066133       0.0000       0.0000 0.0032
##  [13,]   -0.014081172487  0.39448411       0.0000       0.0000 0.0032
##  [14,]   -0.004728048444  0.43587946       0.0000       0.0000 0.0012
##  [15,]   -0.058079904175  1.37959511       0.0000       0.0000 0.0044
##  [16,]    0.001544616464  0.42371313       0.0000       0.0000 0.0020
##  [17,]   -0.040732695240  0.86986619       0.0000       0.0000 0.0044
##  [18,]   -0.006865557049  0.21533116       0.0000       0.0000 0.0024
##  [19,]   -0.011998894558  0.43182955       0.0000       0.0000 0.0032
##  [20,]   -0.008361691197  0.30970124       0.0000       0.0000 0.0028
##  [21,]   -0.006970104828  0.26660794       0.0000       0.0000 0.0028
##  [22,]   -0.007007965690  0.23325519       0.0000       0.0000 0.0016
##  [23,]   -0.040396262965  0.63565151       0.0000       0.0000 0.0060
##  [24,]   -0.020959624209  0.54080109       0.0000       0.0000 0.0024
##  [25,]   -0.021724730863  0.51478822       0.0000       0.0000 0.0032
##  [26,]   -0.005413860447  0.18892482       0.0000       0.0000 0.0016
##  [27,]   -0.029738397069  0.55751700       0.0000       0.0000 0.0044
##  [28,]   -0.023196115574  0.79488927       0.0000       0.0000 0.0028
##  [29,]    0.008410026464  0.31443422       0.0000       0.0000 0.0028
##  [30,]    0.005992522844  0.52089383       0.0000       0.0000 0.0036
##  [31,]   -0.010836618074  0.46832319       0.0000       0.0000 0.0020
##  [32,]   -0.019366941514  0.41092647       0.0000       0.0000 0.0040
##  [33,]   -0.007073964709  0.35369824       0.0000       0.0000 0.0004
##  [34,]   -0.009533040841  0.20545456       0.0000       0.0000 0.0024
##  [35,]   -0.002044884670  0.11064865       0.0000       0.0000 0.0016
##  [36,]    0.017846464403  0.49706980       0.0000       0.0000 0.0032
##  [37,]   -0.001511884657  0.25735825       0.0000       0.0000 0.0016
##  [38,]   -0.000547793286  0.48696232       0.0000       0.0000 0.0032
##  [39,]   -0.003269810596  0.26115267       0.0000       0.0000 0.0020
##  [40,]   -0.004214310639  0.19912010       0.0000       0.0000 0.0024
##  [41,]   -0.028704990271  0.74822170       0.0000       0.0000 0.0040
##  [42,]   -0.015029729977  0.37392663       0.0000       0.0000 0.0032
##  [43,]    0.029835510680  0.91802632       0.0000       0.0000 0.0024
##  [44,]   -0.017132728645  0.37365305       0.0000       0.0000 0.0032
##  [45,]   -0.026701494317  0.82838209       0.0000       0.0000 0.0040
##  [46,]   -0.020654201914  0.79934797       0.0000       0.0000 0.0032
##  [47,]   -0.004008427956  0.59029421       0.0000       0.0000 0.0028
##  [48,]   -0.029563544537  0.69968752       0.0000       0.0000 0.0032
##  [49,]   -0.009712658446  0.71668238       0.0000       0.0000 0.0032
##  [50,]    0.005051140838  0.51037439       0.0000       0.0000 0.0028
##  [51,]   -0.011254438821  0.29627706       0.0000       0.0000 0.0032
##  [52,]    0.003964949062  0.35243090       0.0000       0.0000 0.0020
##  [53,]    0.046573381788  1.74459203       0.0000       0.0000 0.0040
##  [54,]   -0.007312324753  0.21243923       0.0000       0.0000 0.0024
##  [55,]   -0.011627855194  0.66265755       0.0000       0.0000 0.0028
##  [56,]    0.010200989337  0.47201164       0.0000       0.0000 0.0024
##  [57,]   -0.009058233473  0.28611041       0.0000       0.0000 0.0024
##  [58,]    0.012503107309  0.64921487       0.0000       0.0000 0.0028
##  [59,]    0.008498426314  0.55861658       0.0000       0.0000 0.0028
##  [60,]   -0.013857988794  0.34216890       0.0000       0.0000 0.0032
##  [61,]   -0.002599128811  0.14283681       0.0000       0.0000 0.0020
##  [62,]   -0.033409361123  0.85233212       0.0000       0.0000 0.0036
##  [63,]   -0.027676783795  0.92896280       0.0000       0.0000 0.0032
##  [64,]   -0.000659140940  0.25364346       0.0000       0.0000 0.0020
##  [65,]    0.001733394974  0.22635175       0.0000       0.0000 0.0016
##  [66,]   -0.007860807829  0.23076469       0.0000       0.0000 0.0016
##  [67,]   -0.011956818583  0.37250283       0.0000       0.0000 0.0032
##  [68,]    0.000937261816  0.14082938       0.0000       0.0000 0.0020
##  [69,]   -0.006423707867  0.30986026       0.0000       0.0000 0.0024
##  [70,]   -0.017475748447  0.42127434       0.0000       0.0000 0.0024
##  [71,]    0.012804709078  0.45629833       0.0000       0.0000 0.0032
##  [72,]   -0.001671314769  0.17985171       0.0000       0.0000 0.0016
##  [73,]    0.000658612632  0.43937082       0.0000       0.0000 0.0020
##  [74,]    0.017420848461  0.60014008       0.0000       0.0000 0.0016
##  [75,]   -0.020080414204  0.45119462       0.0000       0.0000 0.0028
##  [76,]   -0.008851317288  0.40565163       0.0000       0.0000 0.0032
##  [77,]   -0.011723376751  0.38630949       0.0000       0.0000 0.0020
##  [78,]   -0.041340352835  0.92628545       0.0000       0.0000 0.0060
##  [79,]   -0.032336387805  0.64657739       0.0000       0.0000 0.0044
##  [80,]   -0.025940433076  0.53424941       0.0000       0.0000 0.0044
##  [81,]   -0.006915207656  0.26363331       0.0000       0.0000 0.0024
##  [82,]   -0.016584083503  0.88943253       0.0000       0.0000 0.0020
##  [83,]   -0.004386522652  0.34890949       0.0000       0.0000 0.0016
##  [84,]   -0.005602540932  0.30335672       0.0000       0.0000 0.0020
##  [85,]    0.028464118672  0.69765595       0.0000       0.0000 0.0036
##  [86,]    0.002222104801  0.37119891       0.0000       0.0000 0.0056
##  [87,]   -0.007093243740  0.20921444       0.0000       0.0000 0.0012
##  [88,]   -0.004806214644  0.20942333       0.0000       0.0000 0.0024
##  [89,]   -0.008151481768  0.21045392       0.0000       0.0000 0.0024
##  [90,]    0.001062292648  0.22314458       0.0000       0.0000 0.0016
##  [91,]    0.006050744360  0.49987919       0.0000       0.0000 0.0032
##  [92,]   -0.009631324061  0.54801399       0.0000       0.0000 0.0012
##  [93,]   -0.005515533266  0.17387850       0.0000       0.0000 0.0012
##  [94,]   -0.002598558231  0.18080552       0.0000       0.0000 0.0020
##  [95,]    0.002378794456  0.11893972       0.0000       0.0000 0.0004
##  [96,]    0.013454093375  0.42284519       0.0000       0.0000 0.0028
##  [97,]   -0.006020974326  0.26723311       0.0000       0.0000 0.0008
##  [98,]   -0.007388329221  0.29598010       0.0000       0.0000 0.0016
##  [99,]   -0.005488423861  0.37897275       0.0000       0.0000 0.0020
## [100,]    0.000347217318  0.42933808       0.0000       0.0000 0.0016
## [101,]   -0.002676813019  0.15342417       0.0000       0.0000 0.0012
## [102,]   -0.005627925173  0.25175851       0.0000       0.0000 0.0024
## [103,]   -0.011844692290  0.48027738       0.0000       0.0000 0.0032
## [104,]   -0.001268329736  0.14999299       0.0000       0.0000 0.0016
## [105,]   -0.001045182003  0.29266520       0.0000       0.0000 0.0024
## [106,]   -0.008521510789  0.25306641       0.0000       0.0000 0.0036
## [107,]   -0.001607109386  0.46397777       0.0000       0.0000 0.0020
## [108,]   -0.002991057059  0.32306413       0.0000       0.0000 0.0012
## [109,]   -0.013203907129  0.26653563       0.0000       0.0000 0.0028
## [110,]   -0.006752793322  0.24854685       0.0000       0.0000 0.0020
## [111,]   -0.002074205569  0.18650003       0.0000       0.0000 0.0016
## [112,]   -0.008867585724  0.42849060       0.0000       0.0000 0.0032
## [113,]    0.022057077844  0.71094971       0.0000       0.0000 0.0016
## [114,]    0.009018884773  0.47724739       0.0000       0.0000 0.0020
## [115,]   -0.008619826009  0.22575406       0.0000       0.0000 0.0016
## [116,]   -0.017847765307  0.50532511       0.0000       0.0000 0.0060
## [117,]   -0.015248694595  0.33725528       0.0000       0.0000 0.0048
## [118,]   -0.000074774992  0.12451043       0.0000       0.0000 0.0012
## [119,]   -0.003282572593  0.18213451       0.0000       0.0000 0.0008
## [120,]   -0.003751740166  0.14635147       0.0000       0.0000 0.0012
## [121,]   -0.007847722896  0.26958008       0.0000       0.0000 0.0028
## [122,]    0.006653098385  0.22623174       0.0000       0.0000 0.0016
## [123,]    0.012660124049  0.45883245       0.0000       0.0000 0.0032
## [124,]   -0.019623772516  0.54933169       0.0000       0.0000 0.0032
## [125,]    0.009684540682  0.42251469       0.0000       0.0000 0.0020
## [126,]    0.008427422254  0.24225644       0.0000       0.0000 0.0036
## [127,]    0.009363123779  0.35982593       0.0000       0.0000 0.0040
## [128,]   -0.005542629144  0.14901338       0.0000       0.0000 0.0020
## [129,]   -0.016123626620  0.38449148       0.0000       0.0000 0.0032
## [130,]   -0.001244918327  0.34023677       0.0000       0.0000 0.0016
## [131,]   -0.029894041262  1.06363563       0.0000       0.0000 0.0024
## [132,]   -0.004302471753  0.25635804       0.0000       0.0000 0.0020
## [133,]   -0.019760522392  0.64591174       0.0000       0.0000 0.0028
## [134,]   -0.000079460152  0.35183797       0.0000       0.0000 0.0020
## [135,]   -0.021561690494  0.52154819       0.0000       0.0000 0.0040
## [136,]   -0.010555391033  0.45399201       0.0000       0.0000 0.0032
## [137,]   -0.010336818633  0.34601287       0.0000       0.0000 0.0032
## [138,]   -0.012928137021  0.46364328       0.0000       0.0000 0.0032
## [139,]   -0.006323032973  0.20545899       0.0000       0.0000 0.0032
## [140,]   -0.018984635457  0.40891705       0.0000       0.0000 0.0040
## [141,]    0.008257402372  0.28602969       0.0000       0.0000 0.0028
## [142,]   -0.017586561025  0.79359099       0.0000       0.0000 0.0020
## [143,]    0.015017855215  0.91237201       0.0000       0.0000 0.0012
## [144,]   -0.013311670511  0.43429038       0.0000       0.0000 0.0028
## [145,]   -0.006586659401  0.53689941       0.0000       0.0000 0.0028
## [146,]    0.003999576191  0.24275307       0.0000       0.0000 0.0016
## [147,]   -0.000294332761  0.44241578       0.0000       0.0000 0.0032
## [148,]    0.005244980228  0.57523955       0.0000       0.0000 0.0032
## [149,]   -0.013032968794  0.36970504       0.0000       0.0000 0.0016
## [150,]   -0.003917044902  0.12556602       0.0000       0.0000 0.0020
## [151,]    0.005781301796  0.24331267       0.0000       0.0000 0.0012
## [152,]    0.284933306458  4.49136701       0.0000       0.0000 0.0076
## [153,]    0.014326929783  0.54250773       0.0000       0.0000 0.0020
## [154,]    0.047834466525  1.16532937       0.0000       0.0000 0.0044
## [155,]   -0.002551890086  0.09171732       0.0000       0.0000 0.0008
## [156,]   -0.021328488629  0.42952927       0.0000       0.0000 0.0032
## [157,]   -0.017699617516  0.53203310       0.0000       0.0000 0.0036
## [158,]   -0.012172056095  0.39001156       0.0000       0.0000 0.0016
## [159,]   -0.072518520013  1.12115609       0.0000       0.0000 0.0052
## [160,]   -0.049943378059  1.01841364       0.0000       0.0000 0.0044
## [161,]   -0.016273023996  0.41280465       0.0000       0.0000 0.0036
## [162,]    0.001403457231  0.33030159       0.0000       0.0000 0.0020
## [163,]    0.001034070682  0.09571430       0.0000       0.0000 0.0008
## [164,]   -0.002312992549  0.08391387       0.0000       0.0000 0.0012
## [165,]   -0.014058402906  0.33647727       0.0000       0.0000 0.0032
## [166,]   -0.024069094626  0.64577300       0.0000       0.0000 0.0036
## [167,]   -0.012639900567  0.68511098       0.0000       0.0000 0.0016
## [168,]   -0.057545954671  1.33160866       0.0000       0.0000 0.0048
## [169,]   -0.004369740508  0.27642141       0.0000       0.0000 0.0020
## [170,]    0.000249790060  0.01033581       0.0000       0.0000 0.0008
## [171,]   -0.004814476616  0.27785058       0.0000       0.0000 0.0020
## [172,]    0.003322371715  0.28304937       0.0000       0.0000 0.0024
## [173,]    0.000262044135  0.34686150       0.0000       0.0000 0.0036
## [174,]    0.000871106246  0.17484055       0.0000       0.0000 0.0016
## [175,]   -0.011997385424  0.52003894       0.0000       0.0000 0.0024
## [176,]    0.000257900068  0.23451631       0.0000       0.0000 0.0016
## [177,]   -0.005419969107  0.19064744       0.0000       0.0000 0.0016
## [178,]   -0.005491961553  0.14912357       0.0000       0.0000 0.0016
## [179,]   -0.006607039834  0.24645460       0.0000       0.0000 0.0028
## [180,]   -0.029074198672  0.95631617       0.0000       0.0000 0.0052
## [181,]   -0.005154792508  0.28380396       0.0000       0.0000 0.0020
## [182,]   -0.005153860213  0.24098062       0.0000       0.0000 0.0020
## [183,]    0.013663074266  0.64420976       0.0000       0.0000 0.0040
## [184,]   -0.011605194220  0.37096131       0.0000       0.0000 0.0052
## [185,]   -0.013849934083  0.36826136       0.0000       0.0000 0.0024
## [186,]   -0.006033723166  0.25128820       0.0000       0.0000 0.0028
## [187,]   -0.017259157601  0.37064532       0.0000       0.0000 0.0044
## [188,]   -0.003139894166  0.28067924       0.0000       0.0000 0.0040
## [189,]   -0.002519755325  0.81605617       0.0000       0.0000 0.0032
## [190,]    0.008864952351  0.56598057       0.0000       0.0000 0.0040
## [191,]    0.005384770334  0.25875965       0.0000       0.0000 0.0012
## [192,]    0.007138326893  0.55395280       0.0000       0.0000 0.0020
## [193,]   -0.017840666323  0.50828940       0.0000       0.0000 0.0028
## [194,]    0.001591985921  0.44204808       0.0000       0.0000 0.0028
## [195,]   -0.035300528439  0.82261060       0.0000       0.0000 0.0044
## [196,]   -0.024519384824  0.54560281       0.0000       0.0000 0.0036
## [197,]    0.005197727320  0.48135796       0.0000       0.0000 0.0020
## [198,]   -0.072993406916  2.70855969       0.0000       0.0000 0.0040
## [199,]   -0.106686672265  2.58655772       0.0000       0.0000 0.0056
## [200,]   -0.013922885884  0.41711426       0.0000       0.0000 0.0032
## [201,]   -0.030182007232  1.37445632       0.0000       0.0000 0.0044
## [202,]   -0.008589080125  0.33250821       0.0000       0.0000 0.0024
## [203,]   -0.513911108382  5.93060287       0.0000       0.0000 0.0112
## [204,]   -0.169300089728  4.48576553       0.0000       0.0000 0.0048
## [205,]   -0.009012214270  0.24289121       0.0000       0.0000 0.0024
## [206,]    0.001445648861  0.53602658       0.0000       0.0000 0.0020
## [207,]   -0.217937327898  5.24829489       0.0000       0.0000 0.0052
## [208,]    0.007625090577  0.31171083       0.0000       0.0000 0.0012
## [209,]   -0.083613705546  2.80630157       0.0000       0.0000 0.0040
## [210,]   -0.001222053184  0.63784675       0.0000       0.0000 0.0036
## [211,]    0.000818557337  0.19043546       0.0000       0.0000 0.0012
## [212,]   -0.005404717725  0.30436478       0.0000       0.0000 0.0016
## [213,]   -0.018157070345  0.46418677       0.0000       0.0000 0.0020
## [214,]   -0.000352446322  0.27685661       0.0000       0.0000 0.0028
## [215,]    0.001287913942  0.32451719       0.0000       0.0000 0.0024
## [216,]   -0.035381068461  0.84390721       0.0000       0.0000 0.0048
## [217,]   -0.047381592294  1.49493553       0.0000       0.0000 0.0036
## [218,]   -1.455952328994 12.99058639       0.0000       0.0000 0.0176
## [219,]   -0.030817248163  1.00289103       0.0000       0.0000 0.0024
## [220,]   -0.002603144483  0.32123639       0.0000       0.0000 0.0028
## [221,]    0.793451871979 13.81447567       0.0000       0.0000 0.0080
## [222,]   -0.133266037431  2.47610346       0.0000       0.0000 0.0068
## [223,]   -0.106045004897  2.47846271       0.0000       0.0000 0.0036
## [224,] -413.952536829998 67.78682177    -545.4373    -280.2294 1.0000
## [225,]   -0.042983374544  1.19605647       0.0000       0.0000 0.0032
## [226,]  313.859656609232 66.41106285     186.1134     429.0020 0.9884
## [227,]   -0.002338759031  1.03991891       0.0000       0.0000 0.0040
## [228,]   -0.005049368903  0.19471758       0.0000       0.0000 0.0016
## [229,]    0.007239818926  0.78103128       0.0000       0.0000 0.0028
## [230,]    0.005413978538  0.30353973       0.0000       0.0000 0.0024
## [231,]   -0.005443387782  0.30750159       0.0000       0.0000 0.0032
## [232,]   -0.011885717260  0.43741590       0.0000       0.0000 0.0012
## [233,]   -0.052652550379  1.31164844       0.0000       0.0000 0.0024
## [234,]    0.553875684813  5.57916141       0.0000       0.0000 0.0128
## [235,]    0.005820637663  0.46242327       0.0000       0.0000 0.0024
## [236,]   -0.010762873319  0.50143139       0.0000       0.0000 0.0036
## [237,]   -0.015476598972  0.69065604       0.0000       0.0000 0.0040
## [238,]   -0.022416688219  0.71064236       0.0000       0.0000 0.0040
## [239,]   -0.002234711973  0.16701385       0.0000       0.0000 0.0012
## [240,]    0.131901264646  5.68418599       0.0000       0.0000 0.0040
## [241,]   -0.007544347900  0.52968167       0.0000       0.0000 0.0024
## [242,]    0.006189476408  0.52340408       0.0000       0.0000 0.0020
## [243,]   -0.031131448337  0.74590793       0.0000       0.0000 0.0036
## [244,]   -0.005354132887  0.29719384       0.0000       0.0000 0.0032
## [245,]   -0.048289438762  1.67673018       0.0000       0.0000 0.0040
## [246,]    0.010495258761  0.36957286       0.0000       0.0000 0.0020
## [247,]    0.006699821147  0.43642319       0.0000       0.0000 0.0020
## [248,]   -0.016307624257  0.70127224       0.0000       0.0000 0.0032
## [249,]   -0.011288030811  0.36915236       0.0000       0.0000 0.0044
## [250,]   -0.005875262912  0.24552623       0.0000       0.0000 0.0020
## [251,]    0.052247400844  2.02169780       0.0000       0.0000 0.0028
## [252,]   -0.014861742176  0.39289750       0.0000       0.0000 0.0048
## [253,]   -0.028156575114  1.17100012       0.0000       0.0000 0.0020
## [254,]   -0.005625391100  0.21726137       0.0000       0.0000 0.0028
## [255,]   -0.005921498013  0.41784148       0.0000       0.0000 0.0032
## [256,]   -0.000327063449  1.14546715       0.0000       0.0000 0.0056
## [257,]   -0.002235771972  0.18495768       0.0000       0.0000 0.0020
## [258,]   -0.008842545059  0.30962339       0.0000       0.0000 0.0032
## [259,]   -0.019963481627  0.63723782       0.0000       0.0000 0.0024
## [260,]   -0.008101374080  0.32091058       0.0000       0.0000 0.0028
## [261,]   -0.031184780663  0.66034277       0.0000       0.0000 0.0052
## [262,]   -0.023329571110  0.71851903       0.0000       0.0000 0.0024
## [263,]    0.016738468078  1.46354683       0.0000       0.0000 0.0036
## [264,]   -0.008120413738  0.20854782       0.0000       0.0000 0.0024
## [265,]   -0.054973616122  1.98947150       0.0000       0.0000 0.0036
## [266,]   -0.016908877278  0.48975138       0.0000       0.0000 0.0028
## [267,]   -0.102040422539  3.19690835       0.0000       0.0000 0.0040
## [268,]   -0.005192096833  0.53705152       0.0000       0.0000 0.0016
## [269,]   -0.002642219004  0.30135422       0.0000       0.0000 0.0024
## [270,]   -0.027413634787  0.84131107       0.0000       0.0000 0.0032
## [271,]   -0.005704982514  0.24556803       0.0000       0.0000 0.0012
## [272,]   -0.042003490577  1.28490102       0.0000       0.0000 0.0028
## [273,]   -0.016892861765  0.43140943       0.0000       0.0000 0.0024
## [274,]   -0.030703693154  0.63897320       0.0000       0.0000 0.0044
## [275,]    0.014873218289  1.09602788       0.0000       0.0000 0.0036
## [276,]    0.004473722127  0.75917336       0.0000       0.0000 0.0040
## [277,]   -0.033547782446  0.86557434       0.0000       0.0000 0.0032
## [278,]    0.013876814949  1.01592292       0.0000       0.0000 0.0028
## [279,]    0.014053491796  0.44948547       0.0000       0.0000 0.0028
## [280,]   -0.020498167717  0.42221869       0.0000       0.0000 0.0044
## [281,]   -0.006973901975  0.24121858       0.0000       0.0000 0.0012
## [282,]   -0.072512828475  2.08343030       0.0000       0.0000 0.0028
## [283,]   -0.007023258113  0.21924317       0.0000       0.0000 0.0012
## [284,]   -0.005652926358  0.34315089       0.0000       0.0000 0.0028
## [285,]   -0.034849128579  0.91371192       0.0000       0.0000 0.0032
## [286,]    0.091447579466  3.29583492       0.0000       0.0000 0.0016
## [287,]   -0.038015595084  0.63782589       0.0000       0.0000 0.0060
## [288,]   -0.036738150510  0.70550863       0.0000       0.0000 0.0052
## [289,]   -0.000502675611  0.20744708       0.0000       0.0000 0.0016
## [290,]   -0.035941668626  1.18193322       0.0000       0.0000 0.0028
## [291,]   -0.018731231759  0.43018489       0.0000       0.0000 0.0028
## [292,]    0.000062858338  0.59726805       0.0000       0.0000 0.0040
## [293,]    0.004365506207  1.54194068       0.0000       0.0000 0.0040
## [294,]   -0.000648807000  0.41504882       0.0000       0.0000 0.0028
## [295,]    0.000581494875  0.27636773       0.0000       0.0000 0.0036
## [296,]   -0.056974839278  2.24197161       0.0000       0.0000 0.0048
## [297,]   -0.004885018820  0.29014288       0.0000       0.0000 0.0020
## [298,]   -0.003099366542  0.33539661       0.0000       0.0000 0.0028
## [299,]   -0.005119605306  0.23739965       0.0000       0.0000 0.0012
## [300,]   -0.080908733788  1.72796051       0.0000       0.0000 0.0048
## [301,]   -0.015102207296  0.62104367       0.0000       0.0000 0.0024
## [302,]   -0.006371518757  0.53148830       0.0000       0.0000 0.0040
## [303,]   -0.028281563642  0.76377238       0.0000       0.0000 0.0048
## [304,]   -0.011662830473  0.34521812       0.0000       0.0000 0.0028
## [305,]    0.000249105305  0.82523229       0.0000       0.0000 0.0020
## [306,]   -0.009621075516  0.28429569       0.0000       0.0000 0.0012
## [307,]   -0.021768879307  0.44097782       0.0000       0.0000 0.0048
## [308,]   -0.023157267031  0.52303861       0.0000       0.0000 0.0028
## [309,]    0.046544753547  3.11656820       0.0000       0.0000 0.0032
## [310,]   -0.009687234750  0.32834564       0.0000       0.0000 0.0024
## [311,]   -0.009653232204  0.27878621       0.0000       0.0000 0.0024
## [312,]   -0.005531807256  0.26864351       0.0000       0.0000 0.0024
## [313,]   -0.001857011844  0.26958072       0.0000       0.0000 0.0020
## [314,]    0.029430416252  1.02318641       0.0000       0.0000 0.0016
## [315,]    0.031049778902  1.68742821       0.0000       0.0000 0.0036
## [316,]   -0.028240697487  0.62115461       0.0000       0.0000 0.0036
## [317,]   -0.011123144331  0.54508326       0.0000       0.0000 0.0020
## [318,]    0.556176644377  8.00093279       0.0000       0.0000 0.0072
## [319,]    0.003224735010  0.23515199       0.0000       0.0000 0.0028
## [320,]   -0.008541968967  0.30936212       0.0000       0.0000 0.0024
## [321,]   -0.012519718194  0.46950090       0.0000       0.0000 0.0020
## [322,]   -0.011096629077  0.85498115       0.0000       0.0000 0.0044
## [323,]   -0.010832158123  0.40842097       0.0000       0.0000 0.0040
## [324,]   -0.003625845611  0.57403107       0.0000       0.0000 0.0040
## [325,]   -0.018117532135  0.50930716       0.0000       0.0000 0.0024
## [326,]   -0.011462289596  0.41615289       0.0000       0.0000 0.0052
## [327,]   -0.021899800199  0.60334739       0.0000       0.0000 0.0032
## [328,]   -0.039508532269  1.12758787       0.0000       0.0000 0.0032
## [329,]    0.011764548118  0.32487044       0.0000       0.0000 0.0020
## [330,]   -0.010310495739  0.28399131       0.0000       0.0000 0.0024
## [331,]   -0.012938728130  0.39117906       0.0000       0.0000 0.0020
## [332,]    0.025996910246  1.86850749       0.0000       0.0000 0.0032
## [333,]    0.001338910802  0.35661129       0.0000       0.0000 0.0016
## [334,]   -0.009817677164  0.27847378       0.0000       0.0000 0.0024
## [335,]    0.001047111504  0.05235558       0.0000       0.0000 0.0004
## [336,]    0.013086230832  1.34975169       0.0000       0.0000 0.0044
## [337,]   -0.003597960428  0.21356619       0.0000       0.0000 0.0020
## [338,]   -0.006537467985  0.62149937       0.0000       0.0000 0.0032
## [339,]   -0.014252236837  0.55911261       0.0000       0.0000 0.0020
## [340,]    0.024921280326  1.53931241       0.0000       0.0000 0.0024
## [341,]    0.001121250902  0.60986444       0.0000       0.0000 0.0024
## [342,]   -0.044685030845  2.36525878       0.0000       0.0000 0.0048
## [343,]   -0.007002643357  0.52138865       0.0000       0.0000 0.0020
## [344,]   -0.021491352021  0.44966312       0.0000       0.0000 0.0052
## [345,]    0.021015217938  1.63568635       0.0000       0.0000 0.0032
## [346,]   -0.009775499065  0.34118026       0.0000       0.0000 0.0020
## [347,]   -0.032107267890  0.91895445       0.0000       0.0000 0.0036
## [348,]   -0.124323888772  2.92008932       0.0000       0.0000 0.0052
## [349,]   -0.010299354631  0.43779484       0.0000       0.0000 0.0012
## [350,]   -0.047366852077  0.78319470       0.0000       0.0000 0.0048
## [351,]    0.010873485756  0.69578564       0.0000       0.0000 0.0020
## [352,]   -0.009724085670  0.26025706       0.0000       0.0000 0.0020
## [353,]   -0.033510660970  1.11742617       0.0000       0.0000 0.0040
## [354,]    0.000956228051  0.14501502       0.0000       0.0000 0.0008
## [355,]   -0.049216626690  1.28396245       0.0000       0.0000 0.0040
## [356,]    0.051915856532  2.00548137       0.0000       0.0000 0.0024
## [357,]   -0.003076907549  0.32421724       0.0000       0.0000 0.0016
## [358,]   -0.006295972052  0.23264502       0.0000       0.0000 0.0012
## [359,]   -0.033697924410  1.22275261       0.0000       0.0000 0.0028
## [360,]    0.011056873449  0.47139041       0.0000       0.0000 0.0024
## [361,]    0.009533927984  0.73395015       0.0000       0.0000 0.0024
## [362,]   -0.012332611260  0.99316882       0.0000       0.0000 0.0020
## [363,]    0.001182413842  0.29596629       0.0000       0.0000 0.0012
## [364,]    0.020287372177  0.89054802       0.0000       0.0000 0.0020
## [365,]    0.005000196641  0.49944676       0.0000       0.0000 0.0028
## [366,]    0.018215293570  1.27246051       0.0000       0.0000 0.0024
## [367,]   -0.021581409652  0.49256064       0.0000       0.0000 0.0024
## [368,]    0.008795051035  0.96832622       0.0000       0.0000 0.0040
## [369,]   -0.001593081951  0.20586494       0.0000       0.0000 0.0016
## [370,]   -0.001436100083  0.38885401       0.0000       0.0000 0.0012
## [371,]   -0.020882789992  1.19190114       0.0000       0.0000 0.0048
## [372,]    0.004545141251  0.14278749       0.0000       0.0000 0.0012
## [373,]   -0.022409579467  0.60851670       0.0000       0.0000 0.0020
## [374,]   -0.005888830549  0.25757989       0.0000       0.0000 0.0024
## [375,]   -0.029429856644  0.59236506       0.0000       0.0000 0.0044
## [376,]   -0.009065581255  0.48067199       0.0000       0.0000 0.0016
## [377,]    0.010034487318  0.35726391       0.0000       0.0000 0.0016
## [378,]    0.004556625450  0.71944033       0.0000       0.0000 0.0028
## [379,]    0.033780365756  1.97012229       0.0000       0.0000 0.0044
## [380,]   -0.009600534295  0.28666388       0.0000       0.0000 0.0028
## [381,]   -0.009892438036  0.28440822       0.0000       0.0000 0.0028
## [382,]   -0.029134832244  0.95365383       0.0000       0.0000 0.0032
## [383,]    0.020105498633  1.11307580       0.0000       0.0000 0.0012
## [384,]   -0.011725814534  0.56710317       0.0000       0.0000 0.0020
## [385,]   -0.030316823549  0.81870321       0.0000       0.0000 0.0028
## [386,]   -0.009244909106  0.23714849       0.0000       0.0000 0.0020
## [387,]   -0.007802634131  0.18628582       0.0000       0.0000 0.0024
## [388,]    0.043107027527  1.92883368       0.0000       0.0000 0.0020
## [389,]   -0.022836332892  0.84608311       0.0000       0.0000 0.0036
## [390,]   -0.006445299055  0.24306075       0.0000       0.0000 0.0020
## [391,]    0.000681243690  0.87658194       0.0000       0.0000 0.0040
## [392,]   -0.004120872299  0.13957431       0.0000       0.0000 0.0016
## [393,]   -0.004575656095  0.42682188       0.0000       0.0000 0.0028
## [394,]   -0.014523816489  0.45650895       0.0000       0.0000 0.0040
## [395,]    0.007256646826  0.39660819       0.0000       0.0000 0.0032
## [396,]   -0.021585162249  0.54429820       0.0000       0.0000 0.0036
## [397,]   -0.003497853657  0.14241938       0.0000       0.0000 0.0012
## [398,]   -0.001058950682  0.34902234       0.0000       0.0000 0.0032
## [399,]   -0.000446814129  0.43866442       0.0000       0.0000 0.0020
## [400,]   -0.013569919219  0.44056841       0.0000       0.0000 0.0024
## [401,]    0.104620778953  3.49489537       0.0000       0.0000 0.0044
## [402,]   -0.056485108394  2.35854911       0.0000       0.0000 0.0032
## [403,]   -0.001632290093  0.24877866       0.0000       0.0000 0.0032
## [404,]   -0.014577692567  0.36713958       0.0000       0.0000 0.0040
## [405,]   -2.299317129571 29.45172090       0.0000       0.0000 0.0100
## [406,]   -0.037372359790  1.08576513       0.0000       0.0000 0.0044
## [407,]    0.014526394700  1.50667907       0.0000       0.0000 0.0020
## [408,]   -0.008572487632  0.32311160       0.0000       0.0000 0.0036
## [409,]   -0.061892497093  1.48399868       0.0000       0.0000 0.0048
## [410,]    0.041779959938  2.19189790       0.0000       0.0000 0.0032
## [411,]   -0.016931888532  0.71032842       0.0000       0.0000 0.0016
## [412,]    0.135688577832  3.08889533       0.0000       0.0000 0.0040
## [413,]   -0.073102225366  1.78555628       0.0000       0.0000 0.0036
## [414,]   -0.028525325486  1.02405640       0.0000       0.0000 0.0024
## [415,]   -0.016322037642  0.50326767       0.0000       0.0000 0.0028
## [416,]   -0.050114300671  2.22562138       0.0000       0.0000 0.0016
## [417,]   -0.043529862982  1.57630646       0.0000       0.0000 0.0020
## [418,]   -0.018704427156  0.65718816       0.0000       0.0000 0.0032
## [419,]   -0.020543294260  0.69784830       0.0000       0.0000 0.0028
## [420,]   -0.015232234695  0.40015357       0.0000       0.0000 0.0048
## [421,]   -0.001662661185  0.09979845       0.0000       0.0000 0.0012
## [422,]   -0.005195180116  0.29559508       0.0000       0.0000 0.0024
## [423,]   -0.003225969001  0.34613487       0.0000       0.0000 0.0028
## [424,]   -0.084425084867  2.28393942       0.0000       0.0000 0.0044
## [425,]   -0.032004858613  1.49084824       0.0000       0.0000 0.0032
## [426,]    0.000699072962  0.29748566       0.0000       0.0000 0.0020
## [427,]    0.004010624110  0.18842944       0.0000       0.0000 0.0016
## [428,]   -0.085149757499  4.22193729       0.0000       0.0000 0.0056
## [429,]   -0.008731790587  0.39139927       0.0000       0.0000 0.0028
## [430,]   -0.007067908262  0.34982765       0.0000       0.0000 0.0012
## [431,]   -0.001117192450  0.69984236       0.0000       0.0000 0.0028
## [432,]   -0.057154746705  1.13962276       0.0000       0.0000 0.0048
## [433,]    0.015534273705  1.43788941       0.0000       0.0000 0.0020
## [434,]   -0.004310178039  0.13211135       0.0000       0.0000 0.0016
## [435,]    0.035611057707  2.10818247       0.0000       0.0000 0.0028
## [436,]   -0.356876885499  5.73388892       0.0000       0.0000 0.0076
## [437,]   -0.006226425740  0.22946309       0.0000       0.0000 0.0008
## [438,]    0.003733229941  0.52679234       0.0000       0.0000 0.0028
## [439,]    0.032239119338  1.74489159       0.0000       0.0000 0.0040
## [440,]   -0.010112383322  0.50036216       0.0000       0.0000 0.0024
## [441,]   -0.000031952276  0.07473700       0.0000       0.0000 0.0012
## [442,]   -0.007444236774  0.23504240       0.0000       0.0000 0.0012
## [443,]   -0.022302837542  1.02693821       0.0000       0.0000 0.0016
## [444,]   -0.021457619538  0.76739228       0.0000       0.0000 0.0048
## [445,]   -0.018825279402  0.68125810       0.0000       0.0000 0.0032
## [446,]   -0.011375470445  0.69412742       0.0000       0.0000 0.0060
## [447,]   -0.006603101778  0.37932816       0.0000       0.0000 0.0028
## [448,]   -0.007630211657  0.32728524       0.0000       0.0000 0.0016
## [449,]   -0.013419850771  0.47711775       0.0000       0.0000 0.0016
## [450,]   -0.053264831064  1.72019756       0.0000       0.0000 0.0028
## [451,]   -0.018478896161  2.06581387       0.0000       0.0000 0.0044
## [452,]    0.011009077081  1.25051015       0.0000       0.0000 0.0032
## [453,]   -0.013302121998  0.82676418       0.0000       0.0000 0.0024
## [454,]   -0.007962168908  0.68389037       0.0000       0.0000 0.0036
## [455,]   -0.004655762654  0.25972042       0.0000       0.0000 0.0020
## [456,]   -0.352126588037  4.96926441       0.0000       0.0000 0.0088
## [457,]   -0.147247224477  2.85370254       0.0000       0.0000 0.0080
## [458,]   -0.147753514922  3.48746297       0.0000       0.0000 0.0048
## [459,]    0.633006129805  7.64068394       0.0000       0.0000 0.0116
## [460,]   -0.009869970822  0.36535128       0.0000       0.0000 0.0016
## [461,]    0.016659902115  0.58134616       0.0000       0.0000 0.0024
## [462,]   -0.056970786291  1.62854070       0.0000       0.0000 0.0048
## [463,]    0.002615042718  0.29839162       0.0000       0.0000 0.0024
## [464,]    0.001555155816  0.27263324       0.0000       0.0000 0.0016
## [465,]    0.000828613049  0.04143065       0.0000       0.0000 0.0004
## [466,]   -0.025919449401  0.71872286       0.0000       0.0000 0.0036
## [467,]   -0.021774172344  0.56955763       0.0000       0.0000 0.0028
## [468,]   -0.023683483009  0.62769418       0.0000       0.0000 0.0028
## [469,]   -0.016057486226  0.59474797       0.0000       0.0000 0.0028
## [470,]   -0.006255510773  0.27523904       0.0000       0.0000 0.0024
## [471,]   -0.031141800176  0.80489472       0.0000       0.0000 0.0028
## [472,]   -0.005892461845  0.33006215       0.0000       0.0000 0.0048
## [473,]   -0.083986658901  2.63104402       0.0000       0.0000 0.0036
## [474,]   -0.008533810773  0.23221115       0.0000       0.0000 0.0024
## [475,]    0.003686971151  0.78069158       0.0000       0.0000 0.0048
## [476,]   -0.003163797113  0.62938739       0.0000       0.0000 0.0040
## [477,]   -0.006147636056  0.27839611       0.0000       0.0000 0.0040
## [478,]   -0.007780992008  0.39661424       0.0000       0.0000 0.0036
## [479,]   -0.093984490440  2.33804116       0.0000       0.0000 0.0036
## [480,]   -0.142000201014  3.19632623       0.0000       0.0000 0.0052
## [481,]   -0.060769728387  1.80837064       0.0000       0.0000 0.0024
## [482,]    0.249961276510  5.58804373       0.0000       0.0000 0.0044
## [483,]   -0.014810988996  0.56133080       0.0000       0.0000 0.0028
## [484,]   -0.011618544279  0.39359184       0.0000       0.0000 0.0020
## [485,]   -0.018855804139  0.78826902       0.0000       0.0000 0.0020
## [486,]   -0.009757303757  0.27763284       0.0000       0.0000 0.0020
## [487,]   -0.017090283849  0.49216655       0.0000       0.0000 0.0024
## [488,]    0.004925619692  0.38265231       0.0000       0.0000 0.0032
## [489,]   -0.006277207751  0.26881728       0.0000       0.0000 0.0020
## [490,]   -0.027915750860  0.56181334       0.0000       0.0000 0.0048
## [491,]   -0.014800894443  0.50819596       0.0000       0.0000 0.0036
## [492,]   -0.002319115918  0.11595580       0.0000       0.0000 0.0004
## [493,]   -0.003496873201  0.32653376       0.0000       0.0000 0.0028
## [494,]    0.046835424584  1.47953993       0.0000       0.0000 0.0036
## [495,]   -0.010040952447  0.32086340       0.0000       0.0000 0.0016
## [496,]   -0.052951806011  1.67199012       0.0000       0.0000 0.0024
## [497,]   -2.134476424506 27.89928635       0.0000       0.0000 0.0092
## [498,]    0.012077579283  0.89452195       0.0000       0.0000 0.0032
## [499,]   -0.003043603448  0.18340232       0.0000       0.0000 0.0016
## [500,]    0.007856027372  1.63780425       0.0000       0.0000 0.0040
## [501,]   -0.036162904540  1.26308669       0.0000       0.0000 0.0024
## [502,]   -0.017105719787  0.55983922       0.0000       0.0000 0.0032
## [503,]   -0.008242119569  0.30471215       0.0000       0.0000 0.0024
## [504,]   -0.011749154878  0.73044559       0.0000       0.0000 0.0040
## [505,]    0.027489860471  1.49153996       0.0000       0.0000 0.0032
## [506,]   -0.002752652807  1.17236117       0.0000       0.0000 0.0036
## [507,]    0.001869518856  0.22671972       0.0000       0.0000 0.0020
## [508,]   -0.114474111687  3.37194109       0.0000       0.0000 0.0036
## [509,]   -0.000324616770  0.66513730       0.0000       0.0000 0.0032
## [510,]   -0.065670867074  1.38964905       0.0000       0.0000 0.0048
## [511,]   -0.008304330869  0.33705765       0.0000       0.0000 0.0032
## [512,]   -0.021027771451  0.42381202       0.0000       0.0000 0.0040
## [513,]    0.025009818260  0.88721102       0.0000       0.0000 0.0032
## [514,]   -0.008749565674  0.27605469       0.0000       0.0000 0.0020
## [515,]   -0.029175121261  0.98028088       0.0000       0.0000 0.0040
## [516,]   -0.011105180733  1.43992925       0.0000       0.0000 0.0036
## [517,]   -0.029029340105  2.03515559       0.0000       0.0000 0.0040
## [518,]    0.002121782801  0.16762617       0.0000       0.0000 0.0012
## [519,]   -0.012279599003  0.48796095       0.0000       0.0000 0.0028
## [520,]   -2.997726050766 32.32556987       0.0000       0.0000 0.0144
## [521,]   -0.052861807069  1.80840296       0.0000       0.0000 0.0040
## [522,]    0.001908896025  0.22201078       0.0000       0.0000 0.0012
## [523,]    0.008326424483  0.86119823       0.0000       0.0000 0.0044
## [524,]   -0.000696902904  0.45639412       0.0000       0.0000 0.0032
## [525,]   -0.028669030127  1.03147940       0.0000       0.0000 0.0032
## [526,]   -0.027864026782  1.05589509       0.0000       0.0000 0.0028
## [527,]   -0.007077332746  0.35947067       0.0000       0.0000 0.0024
## [528,]   -0.003165066251  0.45788826       0.0000       0.0000 0.0024
## [529,]   -0.025264491998  0.73867709       0.0000       0.0000 0.0028
## [530,]   -0.002407248547  0.19029916       0.0000       0.0000 0.0024
## [531,]   -0.026988671900  0.79296835       0.0000       0.0000 0.0024
## [532,]   -0.027904241688  0.77970081       0.0000       0.0000 0.0020
## [533,]   -0.045185777690  0.90510639       0.0000       0.0000 0.0032
## [534,]   -0.024288847516  0.67639589       0.0000       0.0000 0.0032
## [535,]   -0.038601797467  1.82275941       0.0000       0.0000 0.0036
## [536,]   -0.029216892863  0.80940221       0.0000       0.0000 0.0036
## [537,]   -0.013701789131  0.40933309       0.0000       0.0000 0.0020
## [538,]    0.004075705949  0.45517398       0.0000       0.0000 0.0040
## [539,]   -0.014341698543  0.96308072       0.0000       0.0000 0.0020
## [540,]   -0.009575326272  0.66971146       0.0000       0.0000 0.0032
## [541,]   -0.007060054628  0.28653919       0.0000       0.0000 0.0040
## [542,]   -0.012043606965  0.48746361       0.0000       0.0000 0.0040
## [543,]    0.028314668300  1.78997931       0.0000       0.0000 0.0024
## [544,]    0.007813646949  0.50839276       0.0000       0.0000 0.0024
## [545,]   -0.001981511014  0.33872398       0.0000       0.0000 0.0032
## [546,]   -0.012736900650  1.02289589       0.0000       0.0000 0.0032
## [547,]   -0.010363716157  0.52285516       0.0000       0.0000 0.0032
## [548,]   -0.031452684510  0.78104597       0.0000       0.0000 0.0044
## [549,]    0.004305775664  1.36258244       0.0000       0.0000 0.0024
## [550,]   -0.129130008040  2.68862453       0.0000       0.0000 0.0056
## [551,]    0.080531446342  2.55519454       0.0000       0.0000 0.0036
## [552,]   -0.044850547770  0.69137476       0.0000       0.0000 0.0060
## [553,]   -0.023004188346  0.73190230       0.0000       0.0000 0.0040
## [554,]   -0.008586678755  0.47770567       0.0000       0.0000 0.0032
## [555,]    0.000002068235  0.07939632       0.0000       0.0000 0.0016
## [556,]   -0.019235229621  1.01131797       0.0000       0.0000 0.0036
## [557,]   -0.004545667809  0.14004592       0.0000       0.0000 0.0012
## [558,]   -0.017375945864  0.45686944       0.0000       0.0000 0.0044
## [559,]   -0.015705037547  0.32676441       0.0000       0.0000 0.0028
## [560,]   -0.024787818199  0.53910394       0.0000       0.0000 0.0028
## [561,]   -0.011438101184  0.72133796       0.0000       0.0000 0.0036
## [562,]   -0.072383085434  1.52664383       0.0000       0.0000 0.0040
## [563,]   -0.014467792585  0.69070450       0.0000       0.0000 0.0020
## [564,]   -0.013353464869  0.36235357       0.0000       0.0000 0.0020
## [565,]   -0.303114762368  5.43798302       0.0000       0.0000 0.0060
## [566,]    0.000726386559  0.10260490       0.0000       0.0000 0.0008
## [567,]   -0.038379189583  0.98905875       0.0000       0.0000 0.0028
## [568,]   -0.008404718875  0.24925761       0.0000       0.0000 0.0028
## [569,]   -0.048219126132  1.39119417       0.0000       0.0000 0.0028
## [570,]   -0.002457785742  0.52866129       0.0000       0.0000 0.0040
## [571,]   -0.102958272408  2.38990795       0.0000       0.0000 0.0040
## [572,]   -0.019193101806  1.34281231       0.0000       0.0000 0.0032
## [573,]   -0.396076693746  5.78309796       0.0000       0.0000 0.0092
## [574,]   -0.006313014750  0.41562784       0.0000       0.0000 0.0024
## [575,]   -0.033720494551  0.94647386       0.0000       0.0000 0.0036
## [576,]   -0.011152609663  0.31138895       0.0000       0.0000 0.0040
## [577,]   -0.013059316532  0.61140019       0.0000       0.0000 0.0016
## [578,]   -0.100127876897  2.41655345       0.0000       0.0000 0.0048
## [579,]   -0.008973082135  0.39429415       0.0000       0.0000 0.0044
## [580,]   -0.011030843931  0.26967397       0.0000       0.0000 0.0024
## [581,]   -0.201728789034  3.27176164       0.0000       0.0000 0.0064
## [582,]   -0.041803502023  1.28385285       0.0000       0.0000 0.0032
## [583,]   -0.097971804684  1.67550962       0.0000       0.0000 0.0072
## [584,]   -0.006987558911  0.20523184       0.0000       0.0000 0.0016
## [585,]   -0.006130884904  0.30916311       0.0000       0.0000 0.0016
## [586,]   -0.042517441424  1.09125098       0.0000       0.0000 0.0028
## [587,]   -0.040261410417  1.49989696       0.0000       0.0000 0.0024
## [588,]   -0.003070691183  0.22089697       0.0000       0.0000 0.0024
## [589,]   -0.018134767918  0.60141194       0.0000       0.0000 0.0028
## [590,]   -0.011828056074  0.34018718       0.0000       0.0000 0.0024
## [591,]   -0.010603148848  0.36074802       0.0000       0.0000 0.0040
## [592,]   -0.126385116105  3.19453967       0.0000       0.0000 0.0048
## [593,]    0.004346256392  0.29474449       0.0000       0.0000 0.0028
## [594,]    0.001607894761  0.86622374       0.0000       0.0000 0.0036
## [595,]   -0.006843810579  0.27519376       0.0000       0.0000 0.0036
## [596,]   -0.213985355554  3.97810615       0.0000       0.0000 0.0060
## [597,]    0.103239089171  2.44129021       0.0000       0.0000 0.0036
## [598,]   -0.033178388236  1.34579511       0.0000       0.0000 0.0028
## [599,]   -0.018999757210  0.48023082       0.0000       0.0000 0.0044
## [600,]   -0.020688925033  0.95490308       0.0000       0.0000 0.0028
## [601,]    0.001052383986  0.17934720       0.0000       0.0000 0.0020
## [602,]   -0.000543938060  0.03789731       0.0000       0.0000 0.0008
## [603,]   -0.006890501416  0.23812849       0.0000       0.0000 0.0012
## [604,]   -0.024701774100  0.84993751       0.0000       0.0000 0.0032
## [605,]   -0.018436160595  0.50035996       0.0000       0.0000 0.0020
## [606,]   -0.032711158116  0.77386803       0.0000       0.0000 0.0028
## [607,]   -0.033769528409  0.93590009       0.0000       0.0000 0.0052
## [608,]    0.016533695553  0.88303353       0.0000       0.0000 0.0028
## [609,]   -0.017040950331  0.72590279       0.0000       0.0000 0.0040
## [610,]   -0.000075473388  0.23066715       0.0000       0.0000 0.0020
## [611,]   -0.044911236588  1.00893242       0.0000       0.0000 0.0040
## [612,]   -0.207377264934  6.62336792       0.0000       0.0000 0.0020
## [613,]   -0.015633233961  0.36642989       0.0000       0.0000 0.0028
## [614,]   -0.014466193983  0.48746437       0.0000       0.0000 0.0028
## [615,]   -0.009470066567  0.19916754       0.0000       0.0000 0.0028
## [616,]   -0.011145309563  0.34862780       0.0000       0.0000 0.0016
## [617,]   -0.073694412234  2.01949504       0.0000       0.0000 0.0040
## [618,]   -0.002270744493  0.51013186       0.0000       0.0000 0.0024
## [619,]   -0.051986057943  1.76236121       0.0000       0.0000 0.0040
## [620,]    0.341216508777  4.97323382       0.0000       0.0000 0.0068
## [621,]   -0.029057316208  1.20740489       0.0000       0.0000 0.0044
## [622,]   -0.004170036862  0.25888583       0.0000       0.0000 0.0036
## [623,]   -0.016762095999  0.40390086       0.0000       0.0000 0.0044
## [624,]   -0.008841936632  0.55027973       0.0000       0.0000 0.0020
## [625,]   -0.039895625749  0.86854427       0.0000       0.0000 0.0036
## [626,]   -0.020756836968  0.44238837       0.0000       0.0000 0.0032
## [627,]   -0.091342617027  2.25213631       0.0000       0.0000 0.0052
## [628,]   -0.021496827341  0.52338538       0.0000       0.0000 0.0044
## [629,]   -0.031196556951  0.81346827       0.0000       0.0000 0.0040
## [630,]   -0.009783985344  0.46546275       0.0000       0.0000 0.0040
## [631,]   -0.004560723218  0.23887607       0.0000       0.0000 0.0016
## [632,]    0.022300146074  1.50436254       0.0000       0.0000 0.0012
## [633,]   -0.032713580312  0.92275375       0.0000       0.0000 0.0028
## [634,]   -0.071150894745  1.35655854       0.0000       0.0000 0.0052
## [635,]    0.038541260512  3.00516041       0.0000       0.0000 0.0040
## [636,]   -0.007490317427  0.28593387       0.0000       0.0000 0.0032
## [637,]   -0.008985082498  0.31613161       0.0000       0.0000 0.0020
## [638,]   -0.006528229600  0.37584409       0.0000       0.0000 0.0032
## [639,]    0.005332243328  1.28345259       0.0000       0.0000 0.0036
## [640,]   -0.013339265053  0.54098719       0.0000       0.0000 0.0024
## [641,]    0.007569581779  0.41217586       0.0000       0.0000 0.0036
## [642,]   -0.364544301470  5.57496331       0.0000       0.0000 0.0088
## [643,]    0.804756106851  9.42468385       0.0000       0.0000 0.0120
## [644,]   -0.036964913415  1.46315369       0.0000       0.0000 0.0032
## [645,]   -0.000739854426  0.04456326       0.0000       0.0000 0.0012
## [646,]   -0.007641471135  0.35127714       0.0000       0.0000 0.0032
## [647,]   -0.020616237369  0.80490443       0.0000       0.0000 0.0048
## [648,]   -0.050242804962  1.30316383       0.0000       0.0000 0.0036
## [649,]   -0.008910899720  0.32236444       0.0000       0.0000 0.0032
## [650,]   -0.035852563233  0.83401858       0.0000       0.0000 0.0036

3.4.4 Predict fitted values for each individual

pred.npb3 <- predict(fit.npb3)
fittedvals3 <- pred.npb3$fitted.vals

3.4.5 Plot predicted outcomes against “measured” outcomes

plot(fittedvals3, Y)
abline(a = 0, b = 1, col = "red")

3.5 Fit the NPB model without ozone and without temperature

Only ozone shows up in the NPB model. However, there is some speculation that ozone is just a proxy for some of the other variables. Here I am running the NPB model without ozone or temperature just to see if something else pops up instead.

priors.npb <- priors.npb.24

#' Exposures
colnames(X.scaled)
##  [1] "mean_pm"             "mean_o3"             "mean_temp"          
##  [4] "pct_tree_cover"      "pct_impervious"      "mean_aadt_intensity"
##  [7] "dist_m_tri"          "dist_m_npl"          "dist_m_waste_site"  
## [10] "dist_m_major_emit"   "dist_m_cafo"         "dist_m_mine_well"   
## [13] "cvd_rate_adj"        "res_rate_adj"        "violent_crime_rate" 
## [16] "property_crime_rate" "pct_less_hs"         "pct_unemp"          
## [19] "pct_limited_eng"     "pct_hh_pov"          "pct_poc"
#' Covariates
colnames(W.scaled2)
##  [1] "lat"           "lon"           "lat_lon_int"   "ed_no_hs"     
##  [5] "ed_hs"         "ed_aa"         "ed_4yr"        "low_bmi"      
##  [9] "ovwt_bmi"      "obese_bmi"     "concep_spring" "concep_summer"
## [13] "concep_fall"   "concep_2010"   "concep_2011"   "concep_2012"  
## [17] "concep_2013"   "maternal_age"  "any_smoker"    "smokeSH"      
## [21] "mean_cpss"     "mean_epsd"     "male"
# fit.npb4 <- npb(niter = 5000, nburn = 2500, X = X.scaled[,-c(2,3)], Y = Y, W = W.scaled2,
#                 scaleY = TRUE,
#                 priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb4, file = here::here("Results", "NPB_Birth_Weight_v4a.4.rdata"))

load(here::here("Results", "NPB_Birth_Weight_v4a.4.rdata"))
npb.sum4 <- summary(fit.npb4)

3.5.1 First, main effect regression coefficients with PIPs

rownames(npb.sum4$main.effects) <- colnames(X.scaled[,-c(2,3)])
npb.sum4$main.effects
##                     Posterior Mean        SD 95% CI Lower 95% CI Upper    PIP
## mean_pm                 0.01740483  6.666825    -13.66354    16.261833 0.2588
## pct_tree_cover         -0.42808738  6.557343    -16.07193    14.870785 0.2664
## pct_impervious         -2.98242948  8.784403    -29.50467     8.315785 0.3316
## mean_aadt_intensity    -0.33582811  5.719151    -12.95181    13.143332 0.2432
## dist_m_tri             -0.32784261  6.267080    -15.15440    14.480333 0.2580
## dist_m_npl              0.32661062  6.933992    -13.35060    18.758868 0.2620
## dist_m_waste_site       1.74392766  8.859841    -10.75379    29.415047 0.2868
## dist_m_major_emit      -0.09948045  5.647990    -12.23102    13.491529 0.2452
## dist_m_cafo            -3.47107470 17.884937    -52.96240    17.467822 0.3368
## dist_m_mine_well       -2.78266572  9.539020    -30.03867    10.711788 0.3192
## cvd_rate_adj           -3.05062600  9.576883    -30.91481     9.044841 0.3148
## res_rate_adj           -2.30442258  8.327439    -24.91180     8.452087 0.3104
## violent_crime_rate     -0.21414248  6.094327    -13.88438    13.958877 0.2600
## property_crime_rate    -1.18082454  6.079274    -17.81515    10.538959 0.2608
## pct_less_hs            -1.68535722  8.358050    -22.33047    12.282048 0.2988
## pct_unemp             -21.61340643 27.288321    -85.60404     0.000000 0.6404
## pct_limited_eng        -1.54816907  7.169160    -21.28668    11.274985 0.3024
## pct_hh_pov             -0.82644993  7.254424    -16.95409    13.457831 0.2788
## pct_poc                -1.26695546  8.277818    -21.24654    13.978007 0.2976

3.5.3 Interactions

Next, all of the interactions between exposures or between exposures and covariates

npb.sum4$interactions
##        Posterior Mean         SD 95% CI Lower 95% CI Upper    PIP
##   [1,]  -0.0535398565  0.8554814            0            0 0.0124
##   [2,]  -0.0277599988  0.5874716            0            0 0.0104
##   [3,]   0.0255571941  1.1632129            0            0 0.0124
##   [4,]  -0.0357963402  0.8616498            0            0 0.0128
##   [5,]  -0.0355543254  0.6103949            0            0 0.0104
##   [6,]  -0.0688209405  1.3881109            0            0 0.0116
##   [7,]  -0.0445171591  0.6889427            0            0 0.0104
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## [563,]  -0.0012151227  0.8015779            0            0 0.0096
## [564,]  -0.1421990748  2.2553920            0            0 0.0156
## [565,]  -0.0928661966  1.4907297            0            0 0.0168
## [566,]   0.0011348669  1.0296102            0            0 0.0092
## [567,]   0.0101763584  1.0693678            0            0 0.0152
## [568,]  -0.0586740331  1.1111645            0            0 0.0132
## [569,]  -0.0684125029  1.2679190            0            0 0.0108
## [570,]  -0.1171469421  2.1579338            0            0 0.0120
## [571,]  -0.0273887135  0.5841025            0            0 0.0080
## [572,]   0.0026318322  1.0076667            0            0 0.0092
## [573,]  -0.0426927657  0.7401675            0            0 0.0128
## [574,]  -0.0038601525  0.8015268            0            0 0.0124
## [575,]  -0.0960533659  1.7560535            0            0 0.0136
## [576,]  -0.0467252421  1.1956374            0            0 0.0132
## [577,]  -0.0635958162  1.5575722            0            0 0.0096
## [578,]   0.2653361117  4.2502310            0            0 0.0164
## [579,]  -0.1001262265  2.4042200            0            0 0.0120
## [580,]  -0.0298604533  1.0531657            0            0 0.0140
## [581,]  -0.1457337210  2.9160920            0            0 0.0116
## [582,]   0.0151159682  1.3015951            0            0 0.0096
## [583,]  -0.0531626298  0.6824881            0            0 0.0136
## [584,]  -0.0238795571  0.8771228            0            0 0.0124
## [585,]  -0.0805775292  1.3170263            0            0 0.0156
## [586,]  -0.0352694022  0.7153470            0            0 0.0140
## [587,]  -0.1278110778  1.4612132            0            0 0.0164
## [588,]  -0.0585217288  1.3671481            0            0 0.0100
## [589,]  -0.0537305557  1.2121609            0            0 0.0132
## [590,]   0.0497467631  2.0005320            0            0 0.0100
## [591,]  -0.0364791537  0.9034047            0            0 0.0164
## [592,]  -0.1214194993  2.0566505            0            0 0.0180
## [593,]  -0.1129100161  2.5673314            0            0 0.0164
## [594,]  -0.0167547914  0.4065176            0            0 0.0112
## [595,]  -0.0600656663  2.2413575            0            0 0.0136
## [596,]  -0.0731911175  1.7236169            0            0 0.0124
## [597,]  -0.0022971184  0.9686253            0            0 0.0128
## [598,]  -0.1751888479  3.4273102            0            0 0.0156
## [599,]  -0.0276795540  0.8566947            0            0 0.0112
## [600,]  -0.4735701251  6.5896271            0            0 0.0200
## [601,]   0.4192674309  5.9960167            0            0 0.0180
## [602,]  -0.0787735480  1.7553057            0            0 0.0132
## [603,]  -0.0332669479  0.8107603            0            0 0.0100
## [604,]  -0.0831124467  2.2230469            0            0 0.0152
## [605,]  -0.0062627532  0.8298027            0            0 0.0096
## [606,]  -0.0782849945  1.2650414            0            0 0.0112
## [607,]  -0.0560609597  0.7830587            0            0 0.0148
## [608,]  -0.0234426753  0.6803685            0            0 0.0116

3.5.4 Predict fitted values for each individual

pred.npb4 <- predict(fit.npb4)
fittedvals4 <- pred.npb4$fitted.vals

3.5.5 Plot predicted outcomes against “measured” outcomes

plot(fittedvals4, Y)
abline(a = 0, b = 1, col = "red")

4 Linear model with the ozone and temperature predictors

The standard deviation of the mean_o3 variable is 3.06 ppb The standard deviation of the mean_temp variable is 4.54 degrees F

lm_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(lm_df)
##  [1] "birth_weight"  "mean_o3"       "mean_temp"     "lat"          
##  [5] "lon"           "lat_lon_int"   "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] "maternal_age"  "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     "male"
#names(lm_df)[2] <- "mean_o3"

head(lm_df)
bw_lm <- lm(birth_weight ~ mean_o3 + mean_temp + mean_o3*mean_temp +
              lat + lon + lat_lon_int +
              ed_no_hs + ed_hs + ed_aa + ed_4yr + 
              low_bmi + ovwt_bmi + obese_bmi + 
              concep_spring + concep_summer + concep_fall +
              concep_2010 + concep_2011 + concep_2012 + concep_2013 +
              maternal_age + any_smoker + smokeSH + 
              mean_cpss + mean_epsd + male,
              data = lm_df)

summary(bw_lm)
## 
## Call:
## lm(formula = birth_weight ~ mean_o3 + mean_temp + mean_o3 * mean_temp + 
##     lat + lon + lat_lon_int + ed_no_hs + ed_hs + ed_aa + ed_4yr + 
##     low_bmi + ovwt_bmi + obese_bmi + concep_spring + concep_summer + 
##     concep_fall + concep_2010 + concep_2011 + concep_2012 + concep_2013 + 
##     maternal_age + any_smoker + smokeSH + mean_cpss + mean_epsd + 
##     male, data = lm_df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1916.84  -299.83    22.74   322.87  1452.55 
## 
## Coefficients:
##                    Estimate Std. Error t value             Pr(>|t|)    
## (Intercept)        2930.492    491.139   5.967        0.00000000352 ***
## mean_o3            -111.268     54.733  -2.033             0.042364 *  
## mean_temp            84.994     54.223   1.568             0.117361    
## lat               -5567.372  17614.332  -0.316             0.752025    
## lon                2639.415   8294.781   0.318             0.750408    
## lat_lon_int       -6721.801  21280.722  -0.316             0.752182    
## ed_no_hs             89.580     72.416   1.237             0.216416    
## ed_hs                64.452     64.814   0.994             0.320305    
## ed_aa                11.513     57.570   0.200             0.841537    
## ed_4yr               73.862     50.607   1.460             0.144782    
## low_bmi             -91.668     92.115  -0.995             0.319944    
## ovwt_bmi             34.637     39.873   0.869             0.385256    
## obese_bmi           111.890     45.156   2.478             0.013406 *  
## concep_spring      -140.315     58.043  -2.417             0.015835 *  
## concep_summer       -68.668     75.272  -0.912             0.361883    
## concep_fall          20.815     72.159   0.288             0.773063    
## concep_2010         279.892    492.161   0.569             0.569706    
## concep_2011         272.096    493.065   0.552             0.581196    
## concep_2012         380.688    495.399   0.768             0.442430    
## concep_2013         367.451    492.442   0.746             0.455759    
## maternal_age         73.144     21.736   3.365             0.000799 ***
## any_smoker         -165.074     62.974  -2.621             0.008912 ** 
## smokeSH             -82.686     43.786  -1.888             0.059301 .  
## mean_cpss             8.597     19.625   0.438             0.661458    
## mean_epsd           -49.574     19.979  -2.481             0.013280 *  
## male                169.917     32.395   5.245        0.00000019614 ***
## mean_o3:mean_temp  -153.026     16.805  -9.106 < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 478.6 on 870 degrees of freedom
## Multiple R-squared:  0.198,  Adjusted R-squared:  0.1741 
## F-statistic: 8.263 on 26 and 870 DF,  p-value: < 0.00000000000000022
plot(bw_lm)
## Warning: not plotting observations with leverage one:
##   1

5 Try a GAM with the ozone and temperature predictor

The NPB model above indicates that there might be a signal for ozone. None of the other exposures had a PIP > 0.5. Here I’ve got a GAM with a smoothing term for ozone to see about potential nonlinear effects

library(mgcv)
## Loading required package: nlme
## 
## Attaching package: 'nlme'
## The following object is masked from 'package:dplyr':
## 
##     collapse
## This is mgcv 1.8-33. For overview type 'help("mgcv-package")'.
library(tidymv)

gam_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(gam_df)
##  [1] "birth_weight"  "mean_o3"       "mean_temp"     "lat"          
##  [5] "lon"           "lat_lon_int"   "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] "maternal_age"  "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     "male"
#names(gam_df)[2] <- "mean_o3"

head(gam_df)
bw_gam <- gam(birth_weight ~ s(mean_o3, mean_temp) +
                lat + lon + lat_lon_int +
                ed_no_hs + ed_hs + ed_aa + ed_4yr + 
                low_bmi + ovwt_bmi + obese_bmi + 
                concep_spring + concep_summer + concep_fall +
                concep_2010 + concep_2011 + concep_2012 + concep_2013 +
                maternal_age + any_smoker + smokeSH + 
                mean_cpss + mean_epsd + male,
              data = gam_df, method = "REML")

summary(bw_gam)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## birth_weight ~ s(mean_o3, mean_temp) + lat + lon + lat_lon_int + 
##     ed_no_hs + ed_hs + ed_aa + ed_4yr + low_bmi + ovwt_bmi + 
##     obese_bmi + concep_spring + concep_summer + concep_fall + 
##     concep_2010 + concep_2011 + concep_2012 + concep_2013 + maternal_age + 
##     any_smoker + smokeSH + mean_cpss + mean_epsd + male
## 
## Parametric coefficients:
##                Estimate Std. Error t value     Pr(>|t|)    
## (Intercept)    2643.384    470.694   5.616 0.0000000265 ***
## lat           -3294.013  16926.563  -0.195      0.84575    
## lon            1573.699   7971.155   0.197      0.84354    
## lat_lon_int   -3979.412  20449.817  -0.195      0.84576    
## ed_no_hs         63.422     69.324   0.915      0.36052    
## ed_hs            39.186     62.319   0.629      0.52965    
## ed_aa            13.279     55.127   0.241      0.80970    
## ed_4yr           65.191     48.430   1.346      0.17863    
## low_bmi        -132.488     88.226  -1.502      0.13355    
## ovwt_bmi         47.005     38.220   1.230      0.21909    
## obese_bmi        97.096     43.301   2.242      0.02519 *  
## concep_spring  -100.337     63.277  -1.586      0.11318    
## concep_summer  -191.433     93.314  -2.051      0.04052 *  
## concep_fall     -56.565     91.389  -0.619      0.53611    
## concep_2010     513.215    474.895   1.081      0.28014    
## concep_2011     451.332    475.951   0.948      0.34326    
## concep_2012     633.958    477.744   1.327      0.18487    
## concep_2013     572.489    475.387   1.204      0.22882    
## maternal_age     76.051     20.794   3.657      0.00027 ***
## any_smoker     -169.774     60.221  -2.819      0.00493 ** 
## smokeSH         -70.957     41.769  -1.699      0.08972 .  
## mean_cpss         7.023     18.856   0.372      0.70966    
## mean_epsd       -48.229     19.127  -2.521      0.01187 *  
## male            153.527     30.962   4.959 0.0000008571 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                        edf Ref.df     F             p-value    
## s(mean_o3,mean_temp) 20.43  25.18 7.548 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.258   Deviance explained = 29.4%
## -REML = 6643.9  Scale est. = 2.0583e+05  n = 897
library(mgcViz)
## Loading required package: qgam
## Loading required package: rgl
## Registered S3 method overwritten by 'GGally':
##   method from   
##   +.gg   ggplot2
## Registered S3 method overwritten by 'mgcViz':
##   method from  
##   +.gg   GGally
## 
## Attaching package: 'mgcViz'
## The following objects are masked from 'package:stats':
## 
##     qqline, qqnorm, qqplot
gam_b <- getViz(bw_gam)
plot(sm(gam_b, 1)) + 
  l_fitRaster() + l_fitContour() + l_points() +
  labs(title = NULL, x = "Ozone (scaled)", y = "Temperature (scaled)") +
  guides(fill=guide_legend(title="Change in\nbirth weight (g)"))

ggsave(filename = here::here("Figs", "Ozone_Temp_GAM_Birth_Weight_v4a.jpeg"),
       device = "jpeg", width = 5, height = 3, units = "in", dpi = 500)  

6 GAM Sensitivity Analysis

The previous GAM suggested a possible nonlinear relationship between ozone and birth weight. However, this might be the influence of abnormally high and low exposures.

Therefore, Ander suggested a sensitivity analysis where we excluded the top and bottom 5% of data and just use the middle 90%.

library(mgcv)

quantile(X.scaled[,"mean_o3"], probs = c(0.05, 0.95))
##        5%       95% 
## -1.568529  1.633168
q_5 <- quantile(X.scaled[,"mean_o3"], probs = c(0.05))
q_95 <- quantile(X.scaled[,"mean_o3"], probs = c(0.95))

gam_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(gam_df)
##  [1] "birth_weight"  "mean_o3"       "mean_temp"     "lat"          
##  [5] "lon"           "lat_lon_int"   "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] "maternal_age"  "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     "male"
head(gam_df)
gam_df2 <- gam_df %>%
  filter(mean_o3 > q_5 & mean_o3 < q_95)
hist(gam_df2$mean_o3)

bw_gam2 <- gam(birth_weight ~ s(mean_o3, mean_temp) + 
                lat + lon + lat_lon_int +
                ed_no_hs + ed_hs + ed_aa + ed_4yr + 
                low_bmi + ovwt_bmi + obese_bmi + 
                concep_spring + concep_summer + concep_fall +
                concep_2010 + concep_2011 + concep_2012 + concep_2013 +
                maternal_age + any_smoker + smokeSH + 
                mean_cpss + mean_epsd + male,
              data = gam_df2, method = "REML")

summary(bw_gam2)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## birth_weight ~ s(mean_o3, mean_temp) + lat + lon + lat_lon_int + 
##     ed_no_hs + ed_hs + ed_aa + ed_4yr + low_bmi + ovwt_bmi + 
##     obese_bmi + concep_spring + concep_summer + concep_fall + 
##     concep_2010 + concep_2011 + concep_2012 + concep_2013 + maternal_age + 
##     any_smoker + smokeSH + mean_cpss + mean_epsd + male
## 
## Parametric coefficients:
##               Estimate Std. Error t value     Pr(>|t|)    
## (Intercept)    2693.68     467.02   5.768 0.0000000116 ***
## lat            1830.07   17945.23   0.102     0.918799    
## lon            -854.75    8450.03  -0.101     0.919455    
## lat_lon_int    2217.23   21680.13   0.102     0.918569    
## ed_no_hs         79.02      72.18   1.095     0.274013    
## ed_hs            48.58      64.37   0.755     0.450659    
## ed_aa            34.44      57.29   0.601     0.547899    
## ed_4yr           41.57      50.41   0.825     0.409820    
## low_bmi        -186.22      90.69  -2.053     0.040362 *  
## ovwt_bmi         36.73      39.67   0.926     0.354802    
## obese_bmi        87.89      45.55   1.930     0.054020 .  
## concep_spring   -63.02      66.02  -0.955     0.340076    
## concep_summer  -133.86      91.72  -1.459     0.144875    
## concep_fall     -46.95      88.85  -0.528     0.597310    
## concep_2010     506.97     470.51   1.077     0.281602    
## concep_2011     467.51     471.84   0.991     0.322077    
## concep_2012     552.20     473.86   1.165     0.244242    
## concep_2013     552.50     471.32   1.172     0.241463    
## maternal_age     77.68      21.73   3.574     0.000374 ***
## any_smoker     -216.85      61.92  -3.502     0.000488 ***
## smokeSH         -70.67      43.61  -1.621     0.105513    
## mean_cpss        13.86      19.71   0.703     0.482190    
## mean_epsd       -49.49      20.02  -2.473     0.013630 *  
## male            130.46      32.28   4.042 0.0000583585 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                       edf Ref.df     F  p-value    
## s(mean_o3,mean_temp) 13.2  17.89 2.727 0.000156 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.151   Deviance explained = 18.9%
## -REML = 5947.4  Scale est. = 2.0255e+05  n = 807
library(mgcViz)
gam_b2 <- getViz(bw_gam2)
plot(sm(gam_b2, 1)) + 
  l_fitRaster() + l_fitContour() + l_points() +
  labs(title = NULL, x = "Ozone (scaled)", y = "Temperature (scaled)") +
  guides(fill=guide_legend(title="Change in\nbirth weight (g)"))

ggsave(filename = here::here("Figs", "Ozone_Temp_GAM_Birth_Weight_Sensitivity_v4a.jpeg"),
       device = "jpeg", width = 5, height = 3, units = "in", dpi = 500)